Evgenii (Eugene) Borisovich Dynkin (obituary)

È. B. Vinberg   ; S. E. Kuznetsov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 2, pp. 345-371

Bibliographie

[1] “O kharakteristicheskikh chislakh stokhasticheskoi matritsy”, Dokl. AN SSSR, 49:3 (1945), 159–162 (with N. Dmitrievym) | MR | Zbl

[2] “Classification of simple Lie groups”, Selected papers of E. B. Dynkin with commentary, eds. A. A. Yushkevich, G. M. Seitz, A. L. Onishchik, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 23–30 | MR | MR | Zbl | Zbl

[3] “O predstavlenii ryada $\log(e^xe^y)$ ot nekommutiruyuschikh $x$ i $y$ cherez kommutatory”, Matem. sb., 25(67):1 (1949), 155–162 | MR | Zbl

[4] “Normed Lie algebras and analytic groups”, Amer. Math. Soc. Transl., 97, Amer. Math. Soc., Providence, RI, 1953, 66 pp. | MR | Zbl

[5] “Avtomorfizmy poluprostykh algebr Li”, Dokl. AN SSSR, 76:5 (1951), 629–632 | MR | Zbl

[6] “Necessary and sufficient statistics for a family of probabiity distributions”, Select. Transl. Math. Statist. Probab., 1, Amer. Math. Soc., Providence, RI, 1961, 17–40 | MR | Zbl

[7] “Maximal subgroups of the classical groups”, Amer. Math. Soc. Transl. (2), 6, Amer. Math. Soc., Providence, RI, 1957, 245–378 | MR | Zbl

[8] “Semisimple subalgebras of semisimple Lie algebras”, Amer. Math. Soc. Transl. (2), 6, Amer. Math. Soc., Providence, RI, 1957, 111–243 | MR | Zbl

[9] “Kriterii nepreryvnosti i otsutstviya razryvov vtorogo roda dlya traektorii markovskogo sluchainogo protsessa”, Izv. AN SSSR. Ser. matem., 16:6 (1952), 563–572 | MR | Zbl

[10] “Homologies of compact Lie groups”, Amer. Math. Soc. Transl. (2), 12, Amer. Math. Soc., Providence, RI, 1959, 251–300 | MR | MR | Zbl | Zbl

[11] “Topological characteristics of homomorphisms of compact Lie groups”, Amer. Math. Soc. Transl. (2), 12, Amer. Math. Soc., Providence, RI, 1959, 301–342 | MR | MR | Zbl | Zbl

[12] “Some limit theorems for sums of independent random variables with infinite mathematical expectations”, Select. Transl. Math. Statist. Probab., 1, Amer. Math. Soc., Providence, RI, 1961, 171–189 | MR | Zbl

[13] “Strong Markov processes”, Theory Probab. Appl., 1:1 (1956), 134–139 (with A. A. Yushkevich) | DOI | Zbl

[14] Osnovaniya teorii markovskikh protsessov, Fizmatgiz, M., 1959, 227 pp. ; Theory of Markov processes, Pergamon Press, Oxford–London–New York–Paris, 1961, 210 СЃ. ; Die Grundlagen der Theorie der Markoffschen Prozesse, Grundlehren Math. Wiss., 108, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1961, xi+174 pp. ; Théorie des processus Markoviens, Collection universitaire de mathématiques, 11, Dunod, Paris, 1963, 214 pp. | MR | Zbl | Zbl | Zbl | Zbl

[15] “Markovskie protsessy i svyazannye s nimi zadachi analiza”, UMN, 15:2(92) (1960), 3–24 ; “Markov processes and related problems of analysis”, Russian Math. Surveys, 15:2 (1960), 1–21 ; ; Magyar Tud. Akad. Mat. Fiz. Oszt. Kozl., 17 (1967), 231–251 | MR | Zbl | DOI | DOI | Zbl

[16] “Random walk on groups with a finite number of generators”, Soviet Math. Dokl., 2 (1961), 399–402 (with M. B. Malyutov) ; Selected papers of E. B. Dynkin with commentary, eds. A. A. Yushkevich, G. M. Seitz, A. L. Onishchik, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 481–484 | MR | MR | Zbl | Zbl

[17] Markov processes, v. I, II, Grundlehren Math. Wiss., 121, 122, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1965, xii+365 pp., viii+274 pp. | MR | MR | Zbl | Zbl

[18] “Markov processes and problems in analysis”, Amer. Math. Soc. Transl. (2), 31, Amer. Math. Soc., Providence, RI, 1963, 1–24 | MR | Zbl

[19] “The optimum choice of the instant for stopping a Markov process”, Soviet Math. Dokl., 4 (1963), 627–629 ; Selected papers of E. B. Dynkin with commentary, eds. A. A. Yushkevich, G. M. Seitz, A. L. Onishchik, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 485–488 | MR | Zbl | Zbl

[20] “Martin boundaries and non-negative solutions of a boundary value problem with a directional derivative”, Russian Math. Surveys, 19:5 (1964), 1–48 | DOI | MR | MR | Zbl

[21] “Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace–Beltrami operator”, Amer. Math. Soc. Transl. (2), 72, Amer. Math. Soc., Providence, RI, 1968, 203–228 | MR | Zbl

[22] “General supplementary conditions for boundary value problems with oblique derivative”, Soviet Math. Dokl., 7:4 (1966), 712–714 ; “РџРёСЃСЊРјРѕ РІ СЂРμдакцию”, 13:2 (1968), 379 | Zbl | MR

[23] “General boundary conditions for denumerable Markov processes”, Theory Probab. Appl., 12:2 (1967), 187–221 | DOI | MR | MR | Zbl

[24] “Diffusion of tensors”, Soviet Math. Dokl., 9 (1968), 532–535 | MR | Zbl

[25] “On the starting points of incursions of Markov processes”, Theory Probab. Appl., 13:3 (1968), 468–470 (with A. A. Yushkevich) | DOI | MR | Zbl

[26] “On extensions of a Markov process”, Theory Probab. Appl., 13:4 (1968), 672–676 | DOI | MR | Zbl

[27] “Boundary theory for Markov processes. (The discrete case)”, Russian Math. Surveys, 24:2 (1969), 1–42 | DOI | MR | Zbl

[28] “The space of exits of a Markov process”, Russian Math. Surveys, 24:4 (1969), 89–157 | DOI | MR | Zbl

[29] “Game variant of a problem on optimal stopping”, Soviet Math. Dokl., 10 (1969), 270–274 | MR | Zbl

[30] “The initial and final behaviour of the trajectories of Markov processes”, Russian Math. Surveys, 26:4 (1971), 165–185 | DOI | MR | Zbl

[31] “Wanderings of a Markov process”, Theory Probab. Appl., 16:3 (1971), 401–428 | DOI | MR | Zbl

[32] “Integral representation of excessive measures and excessive functions”, Russian Math. Surveys, 27:1 (1972), 43–84 | DOI | MR | Zbl

[33] “Regular Markov processes”, Russian Math. Surveys, 28:2 (1973), 33–64 | DOI | MR | Zbl

[34] “Markov representations of stochastic systems”, Russian Math. Surveys, 30:1 (1975), 65–104 | DOI | MR | Zbl

[35] Controlled Markov processes, Grundlehren Math. Wiss., 235, Springer-Verlag, Berlin–New York, 1979 (with A. A. Yushkevich), xvii+289 pp. | MR | MR | Zbl

[36] “Sufficient statistics and extreme points”, Ann. Probab., 6:5 (1978), 705–730 | DOI | MR | Zbl

[37] “Markov processes and random fields”, Bull. Amer. Math. Soc. (N. S.), 3:3 (1980), 975–999 | DOI | MR | Zbl

[38] “Markov processes, random fields and Dirichlet spaces”, Phys. Rep., 77:3 (1981), 239–247 | DOI | MR

[39] “Green's and Dirichlet spaces associated with fine Markov processes”, J. Funct. Anal., 47:3 (1982), 381–418 | DOI | MR | Zbl

[40] “Markov processes as a tool in field theory”, J. Funct. Anal., 50:2 (1983), 167–187 | DOI | MR | Zbl

[41] “Gaussian and non-Gaussian random fields associated with Markov processes”, J. Funct. Anal., 55:3 (1984), 344–376 | DOI | MR | Zbl

[42] “Random fields associated with multiple points of the Brownian motion”, J. Funct. Anal., 62:3 (1985), 397–434 | DOI | MR | Zbl

[43] “Self-intersection gauge for random walks and for Brownian motion”, Ann. Probab., 16:1 (1988), 1–57 | DOI | MR | Zbl

[44] An introduction to branching measure-valued processes, CRM Monogr. Ser., 6, Amer. Math. Soc., Providence, RI, 1994, x+134 pp. | MR | Zbl

[45] “Branching measure-valued processes”, Probab. Theory Related Fields, 99:1 (1994), 55–96 (with S. E. Kuznetsov, A. V. Skorokhod) | DOI | MR | Zbl

[46] “Superdiffusions and removable singularities for quasilinear partial differential equations”, Comm. Pure Appl. Math., 49:2 (1996), 125–176 (with S. E. Kuznetsov) | 3.0.CO;2-G class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[47] “Linear additive functionals of superdiffusions and related nonlinear P.D.E.”, Trans. Amer. Math. Soc., 348:5 (1996), 1959–1987 (with S. E. Kuznetsov) | DOI | MR | Zbl

[48] “Natural linear additive functionals of superprocesses”, Ann. Probab., 25:2 (1997), 640–661 (with S. E. Kuznetsov) | DOI | MR | Zbl

[49] “Fine topology and fine trace on the boundary associated with a class of semilinear differential equations”, Comm. Pure Appl. Math., 51:8 (1998), 897–936 (with S. E. Kuznetsov) | 3.0.CO;2-0 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[50] “Extinction of superdiffusions and semilinear PDEs”, J. Funct. Anal., 162:2 (1999), 346–378 (with S. E. Kuznetsov) | DOI | MR | Zbl

[51] Selected papers of E. B. Dynkin with commentary, eds. A. A. Yushkevich, G. M. Seitz, A. L. Onishchik, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, xxvi+798 pp. | MR | Zbl

[52] Diffusions, superdiffusions and partial differential equations, Amer. Math. Soc. Colloq. Publ., 50, Amer. Math. Soc., Providence, RI, 2002, xii+236 pp. | MR | Zbl

[53] Superdiffusions and positive solutions of nonlinear partial differential equations, Univ. Lecture Ser., 34, Amer. Math. Soc., Providence, RI, 2004, vi+120 pp. | DOI | MR | Zbl

[54] “Harmonic functions and exit boundary of superdiffusion”, J. Funct. Anal., 206:1 (2004), 33–68 | DOI | MR | Zbl

[55] “On extreme $X$-harmonic functions”, Math. Res. Lett., 13:1 (2006), 59–69 | DOI | MR | Zbl

[56] “A note on $X$-harmonic functions”, Illinois J. Math., 50:1-4 (2006), 385–394 | MR | Zbl

[57] “Enhanced Dynkin diagrams and Weyl orbits”, Transform. Groups, 15:4 (2010), 813–841 (with A. N. Minchenko) | DOI | MR | Zbl

[58] E. M. Andreev, É. B. Vinberg, A. G. Élashvili, “Orbits of greatest dimension of semisimple linear Lie groups”, Funct. Anal. Appl., 1:4 (1967), 257–261 | DOI | MR | Zbl

[59] A. Beurling, J. Deny, “Dirichlet spaces”, Proc. Nat. Acad. Sci. U.S.A., 45 (1959), 208–215 | DOI | MR | Zbl

[60] R. M. Blumenthal, “An extended Markov property”, Trans. Amer. Math. Soc., 85 (1957), 52–72 | DOI | MR | Zbl

[61] A. Borel, J. de Siebenthal, “Les sous-groupes fermés de rang maximum des groupes de Lie clos”, Comment. Math. Helv., 23 (1949), 200–221 | DOI | MR | Zbl

[62] H. Cartan, “Théorie générale du balayage en potentiel newtonien”, Ann. Univ. Grenoble. Sect. Sci. Math. Phys. (N. S.), 22 (1946), 221–280 | MR | Zbl

[63] K. L. Chung, “Some new developments in Markov chains”, Trans. Amer. Math. Soc., 81 (1956), 195–210 | DOI | MR | Zbl

[64] D. A. Dawson, “Stochastic evolution equations and related measure processes”, J. Multivariate Anal., 5 (1975), 1–52 | DOI | MR | Zbl

[65] J. L. Doob, “Markoff chains – denumerable case”, Trans. Amer. Math. Soc., 58:3 (1945), 455–473 | DOI | MR | Zbl

[66] J. L. Doob, “Semimartingales and harmonic functions”, Trans. Amer. Math. Soc., 77 (1954), 86–121 | DOI | MR | Zbl

[67] A. G. Élashvili, “Canonical form and stationary subalgebras of points in general position for simple linear Lie groups”, Funct. Anal. Appl., 6:1 (1972), 44–53 | DOI | MR | Zbl

[68] I. V. Evstigneev, “Dynkin's work in mathematical economics”, Selected papers of E. B. Dynkin with commentary, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 793–796

[69] W. Feller, “The parabolic differential equations and the associated semi-groups of transformations”, Ann. of Math. (2), 55:3 (1952), 468–519 | DOI | MR | Zbl

[70] W. Feller, “On boundaries and lateral conditions for the Kolmogorov differential equations”, Ann. of Math. (2), 65:3 (1957), 527–570 | DOI | MR | Zbl

[71] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet forms and symmetric Markov processes, de Gruyter Stud. Math., 19, Walter de Gruyter Co., Berlin, 1994, x+392 pp. | MR | Zbl

[72] G. A. Hunt, “Some theorems concerning Brownian motion”, Trans. Amer. Math. Soc., 81:2 (1956), 294–319 | DOI | MR | Zbl

[73] G. A. Hunt, “Markoff processes and potentials. I, II, III”, Illinois J. Math., 1, 2 (1957, 1958), 44–93, 316–369, 151–213 | MR | Zbl | Zbl

[74] K. Ito, “The Brownian motion and tensor fields on Riemannian manifold”, Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm, 1963, 536–539 | MR | Zbl

[75] N. Jacobson, “Completely reducible Lie algebras of linear transformations”, Proc. Amer. Math. Soc., 2 (1951), 105–113 | DOI | MR | Zbl

[76] F. I. Karpelevich, “O nepoluprostykh maksimalnykh podalgebrakh poluprostykh algebr Li”, Dokl. AN SSSR, 76:6 (1951), 775–778 | Zbl

[77] J. R. Kinney, “Continuity properties of sample functions of Markov processes”, Trans. Amer. Math. Soc., 74:2 (1953), 280–302 | DOI | MR | Zbl

[78] B. Kostant, “The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group”, Amer. J. Math., 81:4 (1959), 973–1032 | DOI | MR | Zbl

[79] S. E. Kuznetsov, “Construction of Markov processes with random birth and death times”, Theory Probab. Appl., 18:3 (1974), 571–575 | DOI | MR | Zbl

[80] S. E. Kuznetsov, “On the decomposition of excessive functions”, Soviet Math. Dokl., 15 (1974), 121–124 | Zbl

[81] J.-F. Le Gall, “The Brownian snake and solutions of $\Delta u=u^2$ in a domain”, Probab. Theory Related Fields, 102:3 (1995), 393–432 | DOI | MR | Zbl

[82] J.-F. Le Gall, “A probabilistic Poisson representation for positive solutions of $\Delta u=u^2$ in a planar domain”, Comm. Pure Appl. Math., 50:1 (1997), 69–103 | 3.0.CO;2-E class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[83] M. Marcus, L. Véron, “The precise boundary trace of positive solutions of the equation $\Delta u=u^q$ in the supercritical case”, Perspectives in nonlinear partial differential equations, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007, 345–383 | DOI | MR | Zbl

[84] P. A. Meyer, “Dynkin and the theory of Markov processes”, Selected papers of E. B. Dynkin with commentary, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 763–772

[85] A. N. Minchenko, “The semisimple subalgebras of exceptional Lie algebras”, Trans. Moscow Math. Soc., 67, Amer. Math. Soc., Providence, RI, 2006, 225–259 | DOI | MR | Zbl

[86] V. V. Morozov, “O nilpotentnom elemente v poluprostoi algebre Li”, Dokl. AN SSSR, 36:3 (1942), 91–94 | MR | Zbl

[87] V. V. Morozov, O nepoluprostykh maksimalnykh podgruppakh prostykh grupp, Dokt. diss., Kazanskii un-t, Kazan, 1943, 105 pp.

[88] B. Mselati, Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation, Mem. Amer. Math. Soc., 164, No 798, Amer. Math. Soc., Providence, RI, 2004, xvi+121 pp. | DOI | MR | Zbl

[89] D. I. Panyushev, E. B. Vinberg, “The work of Vladimir Morozov on Lie algebras”, Transform. Groups, 15:4 (2010), 1001–1013 | DOI | MR | Zbl

[90] D. Ray, “Stationary Markov processes with continuous paths”, Trans. Amer. Math. Soc., 82:2 (1956), 452–492 | DOI | MR | Zbl

[91] I. Z. Rozenknop, “Some problems and applications of the homological theory of polynomial ideals”, Trans. Moscow Math. Soc., 13, Amer. Math. Soc., Providence, RI, 1967, 273–358 | MR | Zbl

[92] B. Simon, The $P(\varphi)_2$ Euclidean (quantum) field theory, Princeton Series in Physics, Princeton Univ. Press, Princeton, NJ, 1974, xx+392 pp. | MR | Zbl

[93] K. Symanzik, “Euclidean quantum field theory”, Local quantum theory, Academic Press, New York–London, 1969, 152–226

[94] A. D. Venttsel', “On boundary conditions for multidimensional diffusion processes”, Theory Probab. Appl., 4:2 (1959), 164–177 | DOI | Zbl

[95] A. M. Vershik, “The problem of describing central measures on the path spaces of graded graphs”, Funct. Anal. Appl., 48:4 (2014), 256–271 | DOI | DOI | MR | Zbl

[96] A. M. Vershik, A. V. Malyutin, “Phase transition in the exit boundary problem for random walks on groups”, Funct. Anal. Appl., 49:2 (2015), 86–96 | DOI | DOI | MR | Zbl

[97] E. B. Vinberg, “Classification of homogeneous nilpotent elements of a semisimple graded Lie algebra”, Selecta Math. Soviet., 6 (1987), 15–35 | MR | Zbl | Zbl

[98] È. B. Vinberg, A. G. Èlashvili, “Classification of trivectors of a $9$-dimensional space”, Selecta Math. Soviet., 7:1 (1988), 63–98 | MR | Zbl | Zbl

[99] S. Watanabe, “A limit theorem of branching processes and continuous state branching processes”, J. Math. Kyoto Univ., 8 (1968), 141–167 | MR | Zbl

[100] A. A. Yushkevich, “Dynkin and probability theory”, Selected papers of E. B. Dynkin with commentary, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 385–392

[101] A. A. Yushkevich, “To the history of strong Markov property”, Selected papers of E. B. Dynkin with commentary, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000, 773–776