Publications of Eugene B. Dynkin II, Research
Papers
Here is a list of research papers arranged
chronologically. Parts I and III of the publication list are books
and miscellanea (popular articles, book reviews etc).
Abbreviations
for the principal Russian mathematical journals:
- DAN - Doklady
Akademii Nauk SSSR,
English translation (published by
the American Math. Society) Soviet Mathematics - Doklady.
- MSb -
Mathematicheskii Sbornik,
English translation (published by the American Math. Society) Mathematics of
the USSR - Sbornik.
- IAN - Ivzvestiya
Akademii Nauk SSR, Matematicheskaya Seriya,
English translation (published by
the American Math. Society) Mathematics of the USSR - Izvestija.
- UMN -
Uspekhi Matematicheskikh Nauk,
English Translation (published by the London Math. Soc. and the British
Library) Russian Mathematical Surveys.
- TV - Teoriya
Veroyatnostei i ee Primeneniya,
English Translation (published by the SIAM) Theory of Probability and its
Applications.
List
of Papers
As a rule we refer to the original
Russian publication. Sometimes we mention (in the brackets { }) the volume,
issue and pages of the English translation.
- On the characteristic roots of a stochastic matrix
(with N. A. Dmitriev), DAN 49 (1945), 159-162
- Classification of the simple Lie groups, MSb 18,
3 (60) (1946), 347 - 353
- On characteristic roots of stochastic matrices (with N.
A. Dmitriev), IAN 10 (1946), 167-184
{Amer. Math. Transl. (2), 140 (1988), 57-77}
- An effective construction of Lie groups from Lie
algebras, UMN 2,3 (19) (1947), 192
- The structure of semi-simple Lie algebras, UMN, 2,
4, (20) (1947), 59-127
{Amer. Math. Soc. Transl. (1950),no.17 143 pp}
- Calculation of the coefficients in the Campbell-
Hausdorff formula, DAN57 (1947), 323-326
- Normed Lie algebras and analytic groups, UMN3,
3 (25) (1948), 157 - 158
- On a problem of the probability theory, UMN4,
5 (33) (1949), 183-197
- On the representation by means of commutators of the
series log exey for noncommuting x, y,
MSb25 (67) (1949), 155-162
-
Normed Lie
algebras and analytic groups, UMN5, 1 (35) (1950), 135-186
{Amer. Math. Soc. Transl. Series 1, Vol. 9 (1962), 470-542}
- On relations of inclusion for irreducible subgroups of
the group of matrices, UMN5, 1, (35) (1950), 214
- Some properties of the system of weights of a linear
representation of a semisimple Lie group, DAN71, 2 (1950),
221-224
- Regular semisimple subsalgebras of semisimple Lie
algebras, DAN73, 5 (1950), 877-880
- Maximal subgroups of semisimple Lie groups and the
classification of primitive groups of transformations, DAN75,
3 (1950), 333-336
- On sufficient and necessary statistics for a family of
probability distributions, DAN75, 2 (1950), 161-164
- Automorphisms of semisimple Lie algebras, DAN76,
5 (1951), 629-632
- Necessary and sufficient statistics for a family of
probabiity distributions, UMN6, 1 (41) (1951), 68-90
{Selected Translations in Math. Statist. and Probab., Vol. 1 (1961), 17-40}
- The relations of inclusion between irreducible groups
of linear transformations, DAN78, 1 (1951), 5-7
- On
semisimple subalgebras of semisimple Lie algebras, DAN81, 6
(1951), 987-990
- Maximal subgroups of the classical groups, Trudy
Moscov. Mat. Obsh.1 (1952), 39-166
{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 245-378}
- Semisimple subalgebras of semisimple Lie algebras, MSb30,
(72) (1952), 349-462
{Amer. Math. Soc. Transl., Series 2, Vol. 6 (1957), 111-244}
- Topological invariants of linear representations of the
unitary group, DAN85, 4 (1952), 697-699
- Criteria of continuity and of absence of
discontinuities of the second kind for trajectories of a Markov stochastic
process, IAN16, 6 (1952), 563-572
- Topological invariants of subgroups of the group of
unitary matrices, UMN7, 4 (50)} (1952), 142-143
- A connection between homologies of a compact Lie group
and its subgroups, DAN87, 3 (1952), 333-336
- Classes of equivalent random variables, UMN8,
2 (54) (1953), 125-130
- Construction of primitive cycles in compact Lie groups,
DAN91, 2 (1953), 201-204
- On topology of compact Lie groups, UMN8,
3 (55) (1953), 174-175
- Homologies of compact Lie groups, UMN8, 5
(57) (1953), 73-120
Corrections: UMN 9, 2(60) (1954), 233
{Amer. Math Soc. Transl. Series 2, Vol. 12, 251-300}
- Homological characteristics of homomorphisms of compact
Lie groups, DAN91, 5 (1953), 1007-1009
- On some limit theorems for Markov chains, Ukrain.
Mat. Zhurnal6, 1 (1954), 21-27
- Topological characteristics of homomorphisms of compact
Lie groups, MSb35 (77), 1 (1954), 129-173
{Amer. Math. Soc. Transl., Series 2, Vol. 12 (1959), 301-342}
- Some limit theorems for sums of independent random
variables with infinite mathematical expectations, IAN19
(1955), 247-266
{Selected Transl. in Math. Statist. and Probability, Vol. 1 (1961), IMS-AMS,
171-189}
- Compact global Lie groups (with A. L. Onishchik), UMN10,
4 (66) (1955), 3-74 {Amer. Math. Soc. Transl., Series 2, Vol. 21 (1962),
119-192}
- Functionals of trajectories of Markov stochastic
processes, DAN104, 5 (1955), 691-694
- Infinitesimal operators of Markov stochastic processes,
DAN105, 2 (1955), 206-209
- Continuous one-dimensional Markov processes, DAN105,
3 (1955), 405-408
- On new analytic methods in the theory of Markov
stochastic processes, Vestnik Leningrad. Gos. Univ.10(1955),
no. 11, 69-74
- Markov processes and semi-groups of operators, TV1
(1956), 25-37
- Strong Markov processes (with A. A. Yushkevich), TV1
(1956), 149-155
- Infinitesimal operators of Markov processes, TV1
(1956), 38-60
- Markov processes - continuous parameter, Proceedings
of the Third All-Union Congress of Mathematicians (Moscow, 1956), Vol.2, 44-47
- Inhomogeneous strong Markov processes, DAN113,
2 (1957), 261-263
- Jump Markov processes, TV3, 1 (1958),
41-60
- New methods in the theory of Markov processes, Proceedings
of the Third All-Union Congress of Mathematicians, Vol. 3, Moscow (1959),
334-342
- One-dimensional continuous strong Markov processes, TV4,
1 (1959), 3-54
- Intrinsic topology and excessive functions connected
with a Markov process, DAN127 (1959), 17-19
{Selected Transl. in Math. Statistics and Probability, Vol. 3, 327-330}
- Linear algebra, In Mathematics in the USSR for
40 years, Vol. 1,207-212; GIFML, Moscow,
1959
- Lie groups, In Mathematics in the USSR for
40 years Vol. 1, 213-227; GIFML, Moscow
1959
- Markov processes and related problems of analysis, UMN15,
2 (92) (1960), 3-24,
{Hungarian transl. Magyar Tud. Acad.Mat.Fiz.Oszt.Kozl.17 1967,
231-251}
- Markov processes and their subprocesses, Proceedings
of All-Union Conference on Probability Theory and Math. Statistics (Erevan, 1958), 223-235; Izdat. Akad. Nauk.
Armyan. SSR, Erevan, 1960
- On some transformations of Markov processes, DAN133,
2 (1960), 269-272
- Additive functionals of the Wiener process determined
by stochastic integrals, TV5, 4 (1960), 441-452
- Topologies associated with a Markov process and the
strong Markov property (with I. V. Girsanov), TV5, 3 (1960),
375
- Random walks on groups with a finite number of
generators (with M. B. Malyutov), DAN137, 5 (1961),
1042-1045
- Transformations of Markov processes connected with
additive functions, Proc. 4th Berkeley
Sympos. Math. Statist. and Probability (Berkeley, Calif., 1960), vol.
2, 117-142; University
of California Press,
Berkeley, Calif.
- Non-negative eigenfunctions of the Laplace-Beltrami
operator and Brownian motion in certain symmetric spaces, DAN141,
2 (1961), 288-292
- Brownian motion with killing measure mu and
speed measure nu, DAN144, 3 (1962), 483-486
- Markov processes and problems in analysis, Proc.
Intern. Congress of Mathematicians (Stockholm,
1962), pp 36-58; Inst. Mittag-Leffler, Djursholm, 1963
{Amer. Math. Soc. Transl., Series 2, Vol. 31, 1-24}
- Optimal choice of the stopping time of a Markov
process, DAN150, 2 (1963), 238-240
- Some problems of the theory of differential equations
connected with Markov processes, Outlines Joint Soviet-American Sympos.
Partial Differential Equations (Novosibirsk,
1963), 67-72; Academ. Sci. USSR, Siberian Branch, Moscow 1963
- Non-negative solutions of a boundary value problem with
oblique derivative, DAN157, 5 (1964), 1028-1030
- Martin boundary and non-negative solutions of a
boundary value problem with oblique derivative, UMN19, 5
(119) (1964), 3-50,
Letter to the Editor 19, 6 (120), 255-256
- Martin boundaries, Winter School
of Theory of Probability and Math. Statistics (Uzhgorod, 1964),
87-124; Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1964
- Controlled random sequences, TV10, 1
(1965), 3-18
- Martin boundary and positive solutions of some boundary
value problems, Annales de l'Institut Fourier (Grenoble)15, 1 (1965),
275-282
- Brownian motion in certain symmetric spaces and
non-negative eigenfunctions of the Laplace-Beltrami operator, IAN30,
2 (1966), 455-478
{Amer. Math. Soc. Transl., Series 2, 72 (1968), 203-228}
- General boundary conditions for Markov processes with
denumerable set of states, International Congress of Mathematicians (Moscow, 1966),
Abstracts of Short Communications, Section 11, 35-36
- General additional conditions for a boundary value
problem with oblique derivative, DAN168, 4 (1966), 737-739
- General boundary conditions for denumerable Markov
processes, DAN172, 2 (1967), 258-261
- General boundary conditions for denumerable Markov
processes, TV12, 2 (1967), 222-257;
Letter to the Editor 13, 2 (1967), 379
- General lateral conditions for some diffusion
processes, Proc. 5th Berkeley
Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66;
Vol.2, Part 2, 17-49; Univ.
of California Press,
Berkeley, Calif. 1967
- Diffusion of tensors, DAN179, 6 (1968),
1264-1267
{9,2, 532-535}
- Sufficient statistics for the optimal stopping problem,
TV13, 1 (1968), 150-152
Letter to the Editor TV13, 4 (1968), 755
- On the origins of the wanderings of Markov processes
(with A. A. Yushkevich), TV13, 3 (1968), 490-493
- On extensions of a Markov process TV13, 4
(1968), 708-713
- Martin boundaries, The Fourth Summer School
(Katsiveli, 1966), 5-41, Naukova Dumka, Kiev 1968
- A game version of an optimal stopping problem, DAN185,
1 (1969), 16-19
{10,2, 270-274}
- Boundary theory for Markov processes (discrete case), UMN24,
2 (146) (1969), 3-42
{24, 2, 1-42}
- Exit space of a Markov process, UMN24, 4
(148) (1969), 89-152 {24, 4, 89-157}
- Excessive functions and the exit-space of a Markov
process, TV15, 1 (1970), 38-55
- Classes of similar Markov processes and corresponding
exit and entrance spaces, J. Sci., Univ. Tokyo, Sec. 117,
1-2 (1970), 87-100
- Excessive measures and entrance laws for a Markov
process, MSb84, 2 (126) (1971), 218-253
{13, 2, 209-246}
- Initial and final behaviour of the trajectories of
Markov processes, UMN26, 4 (160) (1971), 153-172
{26, 4 165-185}
- Wanderings of a Markov process, TV16, 3
(1971), 409-436
{16, 401-428}
- Entrance and exit spaces for a Markov Process, Actes
du Congr�s International des Math�maticiens (Nice, 1970), Tome 2,
507-512; Gauthier-Villars, Paris,
1971
- Supermartingales with random birth times, UMN26,
6 (162), 1971, 241-242
- Some probability models for an expanding economy, DAN200
(1971), 523-525
{ 12 , 5, 1422-1425}
- Optimal control for a sequence of sums of independent
random variables, Ekonom. i Mat. Metody7, 6 (1971), 901-903
- Integral representation of excessive measures and
excessive functions, UMN27, 1 (163) (1972), 43-80
{ 27, 1, 43-84}
- Stochastic concave dynamic programming, MSb87
(129), 4 (1972), 490-503
{16, 4, 501-515}
- Regular Markov processes, UMN28, 2 (170)
(1973), 35-64
{28, 2, 33-64}
- Duality in the theory of Markov process, International
Conference on Probability Theory and Mathematical Statistics (Vilnius, 1973),
Abstracts of Communications, Vol. 1, 213-216
- Optimal programs and stimulating prices in the
stochastic models of economic growth, Math. Models in Economics ( Proc.
Sympos. and Conf. on von Neumann Models, Warsaw, 1972) J. \Lo\'s and
M. W. \Lo\'s, eds, pp. 207-218; North-Holland, Amsterdam; Elsevier, New
York; PWN, Warszawa, 1974
- Determining functions of Markov processes and
corresponding dual regular classes (with S. E. Kuznetsov), DAN214,
1 (1974), 25-28
{15, 1 20-23}
- Additive functionals of Markov processes and their
spectral measures, DAN214, 6 (1974), 1241-1244
{15, 1, 330-334}
- Markov representations of stochastic systems, DAN218
(1974), 1009-1012
{15, 5 1442-1446}
- Markov representations of stochastic systems UMN30,
1, (181) (1975), 61-99
{30, 1 64-104}
- Stochastic dynamical models of economic equilibrium, Proc.
of the International Congress of Mathematicians (Vancouver, BC, 1974),
Vol. 2, 509-515; Canad. Math. Congress, Montreal Que, 1975
- On preference relations under uncertainty (with A. I.
Ovseevich), Ekonomika i Mat. Metody 11, 2 (1975), 393-395
- Additive functionals of Markov processes and stochastic
systems, Collection of articles dedicated to Marcel Brelot on the occasion
of his 70th birthday, Ann. Inst. Fourier (Grenoble)25, 3-4 (1975),
177-200
Correction: 26 (1976), no.1, 1 loose p.
- Regular conditional mathematical expectations of
correspondences (with I. V. Evstingneev), TV21, 2 (1976),
334-347
- Economic equilibrium under uncertainity, Computing
Equilibria, How and Why (Proc. Internat. Conf. Comput. Centre, Polish
Acad. Sci. Torun, 1974), J. \Lo's and M. W. \Lo's, eds, pp. 41-60; PWN
(1976); Warszawa; North-Holland, Amsterdam,
1976.
- On a new approach to Markov processes, Proceedings
of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), pp. 42-64. Lecture
Notes in Math., vol. 550, Springer, Berlin
1976.
- Markov systems and their additive functionals, Annals
of Probability5 (1977), 653-677
- Sufficient statistics and extreme points, Ann.
Probab. 6 (1978), 705-730.
{Chinese transl.Yingyong Shuxue yu Jisuan Shuxue 1980, no. 6, 48-65}
- On duality for Markov processes, Stochastic analysis
(Proc. Internat. Conf. Northwestern Univ., Evanston, Ill, 1978) , A.
Friedman and M. Pinsky, eds, pp. 63-77; Academic Press, New York-London,
1978.
- Minimal excessive measures and functions, Trans.
Amer. Math. Soc.258 (1980), 217-244
- Markov processes and random fields, Bull. Amer.
Math. Soc. (N. S.)3, (1980) no.3, 975-999
- Markov processes, random fields and Dirichlet spaces, Physics
Report77, 3 (1980), 239-247
- Additive functionals of several time-reversible Markov
processes, J. Funct. Anal.42, (1980), no. 1, 64-101
- Harmonic functions associated with several Markov
processes, Adv. in Appl. Math.2 (1981), 260-283
- Green's and Dirichlet spaces associated with fine
Markov processes, J. Funct. Anal.47 (1982), no.3, 381-418
- Green's and Dirichlet spaces for a symmetric Markov
transition functions, Probability, Statistics and Analysis, J. F.
C. Kingman and G. E. H. Reuter, eds; pp. 79-98;, London Math. Soc. Lecture
Note Ser. 79; Cambridge
University Press, Cambridge-New York, 1983.
- Stochastic waves (with R. J. Vanderbei), Trans.
Amer. Math. Soc.275 (1983),no.2 771-779
- Markov processes as a tool in field theory, J.
Funct. Anal.50, (1983), no.2, 167-187
- Gaussian random fields and Gaussian evolutions, Theory
and Applications of Random fields (Bangalore, 1982), G. Kallianpur,
ed.,pp. 28-39; Lecture Notes in Control and Information Sci. 49, Springer,
Berlin-New York, 1983.
- Symmetric statistics, Poisson point processes and
multiple Wiener integrals (with A. Mandelbaum), Ann. Statist.11,
(1983),no.3 739-745
- Gaussian and non-Gaussian random fields associated with
Markov processes, J. Funct. Anal.55 (1984), no. 3, 344-376
- Polynomials of the occupation field and related random
fields, J. Funct. Anal.58 (1984), no.1 20-52
- Local times and quantum fields Seminar on Stochastic
Processes (Gainsville,
Fla.) E. Cinlar, K. L.
Chung, R. K. Getoor, eds, pp. 69-83, Birkh�user, Boston, 1984.
- An application of flows to time shift and time reversal
in stochastic processes, Trans. Amer. Math. Soc.287 (1985),
no.2, 613-619
- Random fields associated with multiple points of the
Brownian motion, J. Funct. Anal.62 (1985), no.3, 397-434
- Additive functionals and entrance laws (with R. K.
Getoor), J. Funct. Anal.62 (1985), 221-265
- Multiple path integals, Adv. in Appl. Math.7
(1986), no. 2, 205-219
- Generalized random fields related to self-intersections
of the Brownian motion, Proc. Nat. Acad. Sci. USA83 (1986),
no.11 3573-3576
- Functionals associated with self-intersections of the
planar Brownian motion, S�minaire de Probabilit�s, XX, 1984/85,
pp. 553-571, J. Az�ma, M. Yor, eds; Lecture Notes in Math., 1204,
Springer, Berlin/New York, 1986.
- Self-intersection local times, occupation fields and
stochastic integrals, Adv. in Math.65 (1987), no. 3,
254-271.
- Stochastic processes on random domains (with P. J.
Fitzsimmons), Ann. Inst. H. Poincar� Probab. Statist. 23
(1987),no. 2, suppl. 379-396.
- Regularized self-intersection local times of planar
Brownian motion, Ann. Probab.16 (1988), no. 1, 58-74
- Self-intersection gauge for random walks and for
Brownian motion, Ann. Probab.16 (1988), no. 1, 1-57
- Representation for functionals of superprocesses by
multiple stochastic integrals, with applications to self-intersectional
local times, Colloque Paul L�vy sur le Processus Stochastiques
(Palaiseau, 1987). Ast�risque157-158 (1988), 147-171
- Superprocesses and their linear additive functionals, Trans.
Amer. Math. Soc.314 (1989), 255-282
- Three classes of infinite dimensional diffusions, J.
Funct. Anal.86 (1989), no.1 75-110
- Kolmogorov and theory of Markov processes Ann.
Probab.17 (1989), no. 3, 822-832
- Regular transition functions and regular
superprocesses, Trans. Amer. Math. Soc.316 (1989), no.2,
623-634
- Branching particle systems and superprocesses, Ann.
Probab.19, 3 (1991), 1157-1194
- A probabilistic approach to one class of nonlinear
differential equations, Probab. Theory Rel. Fields 89
(1991), 89-115
- Path processes and historical superprocesses, Probab.
Theory Rel. Fields 90 (1991), no. 1, 1-36
- Additive functionals of superdiffusion processes, Random
Walks, Brownian Motion and Interacting Particle Systems, pp.269-281;
R. Durrett, H. Kesten, eds; Progr. Probab, 28; Birkh�user, Boston, 1991.
- Superdiffusions and parabolic nonlinear differential
equations Ann. Probab.20 (1992), no.2, 942-962
- Birth delay of a Markov process and the stopping
distributions for regular processes, Probab. Theory Rel. Fields 94
(1993), no. 3, 399-411.
- On regularity of superprocesses, Probab. Theory Rel.
Fields 95 (1993), no.2, 263-281
- Superprocesses and partial differential equations (The
1991 Wald Memorial Lecture), Ann. Probab.21 (1993), no. 3,
1185-1262
- Branching measure-valued processes (with S. E.
Kuznetsov and A. V. Skorokhod), Probab. Theory Rel. Fields99 (1994),
55-96
- A type of interaction between superprocesses and
branching particle systems, Measure-valued Processes, Stochastic
Partial Differential Equations and Interacting systems (Montreal 1992) ,
pp.83-86; CRM Monograph Series, vol. 5, ed. D. A. Dawson , Amer. Math.
Soc., Providence, R.I., 1994
- Branching with a single point catalyst, Stochastic
Analysis (Ithaca, N.Y., 1993), Proc. Sympos. Pure Math. 57,
423-425; Amer. Math. Soc., Providence,
R.I., 1995
- Markov snakes and superprocesses (with S. E.
Kuznetsov), Probab. Theor. Rel. Fields , 103 (1995), no.4,
433-473
- Superdiffusions and removable singularities for
quasilinear partial differential equations (with S. E. Kuznetsov), Comm.
Pure Appl.Math.49 (1996), 125-176
- Solutions of Lu =ua dominated by L-harmonic
functions (with S.E. Kuznetsov), J. Anal. Math., 68 (1996),
15-37
- Linear additive functionals of superdiffusions and
related nonlinear P.D.E. (with S.E. Kuznetsov), Trans. Amer. Math. Soc.348
(1996), 1959-1987
- L�vy measure of superprocesses; absorption process, Ito's
Stochastic Calculus and Probability Theory , eds. N.Ikeda, S.Watanabe,
M. Fukushima, H. Kunita, pp. 1-14, Springer Berlin/New York, 1996
- Natural linear additive functionals of superprocesses
(with S.E. Kuznetsov), Ann. Probab., 25 (1997), no. 2,
640-661
- Nonlinear parabolic P.D.E. and additive functionals of
superdiffusions (with S.E. Kuznetsov), Annals Probab., 25
(1997), no. 2, 662-701
- A probabilistic approach to a nonlinear differential equation
on a Riemannian manifold, TV, 42 (1997), 336-341
- Polylinear additive functionals of superprocesses, J.
Functional Analysis, 148 (1997), 148-257
- A new relation between diffusions and superdiffusions
with applications to the equation Lu =ua, C.R. Acad.
Sci. Paris, S�rie I, 35 (1997), 439-444
- Trace on the boundary for solutions of nonlinear
differential equations (with S.E. Kuznetsov), Transactions of Americ.
Math. Soc. , 350 (1998), no. 11, 4499-4519
- Solutions of nonlinear differential equations on a
Riemannian manifold and their trace on the Martin boundary (with
S.E.Kuznetsov), Trans. Americ. Math. Soc. , 350 (1998), no.
11, 4521-4552
- Stochastic boundary values and boundary singularities
for solutions of the equation Lu =ua. J. Functional
Analysis, 153 (1998), 147-186
- Fine topology and fine trace on the boundary associated
with a class of semilinear differential equations (with S. E. Kuznetsov), Comm.
Pure Appl.Math., 51 (1998), 897-936
- Semilinear parabolic equations, diffusions and
superdiffusions, J. Functional Analysis, 158 (1998), 325-356
- Extinction of superdiffusions and semilinear PDEs (with
S. E. Kuznetsov), J. Functional Analysis 162(1999), 346-378
- Solutions of a class of semilinear differential
equations: trace and singularities on the boundary (with S. E. Kuznetsov),
Operator Theory:Advances and Applications110(1999), 69-80
- Exit laws and excessive functions for superprocesses, TV44
(1999), 880-885
- Probability and nonlinear analysis, Canadian Mathematical
Society Conference Proceedings, 28 (2000), 139-144
- Solutions of semilinear equations related to harmonic
functions, J. Functional Analysis 170 (2000),464-474
- A probabilistic approach to the equation Lu =-u2,
J. Functional Analysis 170 (2000),450-463
- Rough boundary trace for solutions of Lu=\psi(u)
(with S.E.Kuznetsov), TV45 (2000),740-744
- Branching exit Markov systems and superprocesses, Annals
Probab. 29 (2001), 1833-1858
- Poisson capacities, Mathematical Research
Letters, 10 (2003), 85-95
- Harmonic functions and exit boundary of superdiffusion,
J. Functional Analysis, 206 (2004), 31-68
- Branching exit Markov systems and their applications to
partial differential equations, In Markov Processes and Controlled
Markov Chains, Zhenting Hou, Jerzy A. P. Filar and Anyue Chen (Eds.),
3-13, Kluver Academic Publishers, Dordrecht/ Boston/ London, 2002
- On upper bounds for positive solutions of semilinear
equations, J. Functional Analysis, 210 (2004), 73-100
- N-measures for branching exit Markov systems and their
applications to differential equations (with S.E.Kuznetsov), Probab.
Theory Relat. Fields, 130 (2004), 135-150
- A new inequality for superdiffusions and its
applications to nonlinear differential equations, Electronic Research
Announcements, AMS, 10 (August 2, 2004), 68-77
- Absolute comtinuity results for superdiffusions with
applications to differential equations, C.R. Acad. Sci. Paris,
Ser. I, 338 (2004), 605-610
- Superdiffusions and positive solutions of nonlinear
partial differential equations, UMN, 59:1(355) (2004),
145-156 (in Russian);: Russian Mathematical Surveys 59:1
(2004), 147-156 (in English)
- On extreme X-harmonic functions, Mathematical
Research Letters, 13 (2006), no. 1, 59-69
- A note on X-harmonic functions, Illinois J. Math.,
50:2 (2006), 385-394
- An application of probability to nonlinear analysis, In:
Stochastic Analysis and Applications, The Abel Symposium 2005,
Springer, 2007, 309-325
- Bessel capacities on compact manifolds and their
relation to Poisson capacities, J. Functional Analysis, 242
(2007), 281-294
- A class of boundary traces for solutions of the
equation Lu=\psi(u), J. Functional Analysis, 252
(2007), 696-709
- Probability theory and analysis (in Russian),Seminar
Globus 4, Seminar of Independent Moscow University,
MCNO-NMU, Moscow, 2009, 209-220
185.
Enhanced Dynkin diagrams and Weyl
orbits (with A. N. Minchenko), Transformation Groups, 15:4 (2010), 813-841
186.
Markov processes and their
applications to partial differential equations Kuznetsov's contributions In: Advances in Superprocesses and Nonlinear
PDEs, Springer 2013
;
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