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@article{THSP_2010_16_2_a4, author = {Yu. E. Gliklikh}, title = {Stochastic dynamics via equations and inclusions in terms of mean derivatives and infinitesimal generators}, journal = {Teori\^a slu\v{c}ajnyh processov}, pages = {33--43}, publisher = {mathdoc}, volume = {16}, number = {2}, year = {2010}, language = {en}, url = {http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a4/} }
TY - JOUR AU - Yu. E. Gliklikh TI - Stochastic dynamics via equations and inclusions in terms of mean derivatives and infinitesimal generators JO - Teoriâ slučajnyh processov PY - 2010 SP - 33 EP - 43 VL - 16 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a4/ LA - en ID - THSP_2010_16_2_a4 ER -
Yu. E. Gliklikh. Stochastic dynamics via equations and inclusions in terms of mean derivatives and infinitesimal generators. Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 33-43. http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a4/
[1] S. V. Azarina, Yu. E. Gliklikh, “Differential inclusions with mean derivatives”, Dynamic Systems and Applications, 16:1 (2007), 49–71
[2] S. V. Azarina, Yu. E. Gliklikh, “Stochastic differential inclusions in terms of infinitesimal generators and mean derivatives”, Applicable Analysis, 88:1 (2009), 89–105
[3] S. V. Azarina, Yu. E. Gliklikh, “Stochastic differential equations and inclusions with mean derivatives relative to the past”, Int. J. of Difference Equations, 4:1 (2009), 27–41
[4] S. V. Azarina, Yu. E. Gliklikh, “Inclusions with mean derivatives for processes of geometric Bowninan motion type and their applications”, Seminar on Global and Stochastic Analysis, 2009, no. 4, 3–8 (in Russian)
[5] S. V. Azarina, Yu. E. Gliklikh, A. V. Obukhovskii, “Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds”, Applicable Analysis, 86:9 (2007), 1105–1116
[6] S. V. Azarina, Yu. E. Gliklikh, A. V. Obukhovskii, “Mechanical systems with random perturbations on non-linear configuration spaces”, Proceedings of Voronezh State University, Series Phys. Math., 2008, no. 1, 205–221
[7] Ya. I. Belopolskaya, Yu. L. Daletskii, Stochastic Processes and Differential Geometry, Kluwer, Dordrecht, 1989
[8] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskiĭ, Introduction to the Theory of Set-Valued Mappings and Differential Inclusions, KomKniga, Moscow, 2005 (in Russian)
[9] E. D. Conway, “Stochastic equations with discontinuous drift”, Trans. Amer. Math. Soc., 157:1 (1971), 235–245
[10] K. D. Elworthy, Stochastic Differential Equations on Manifolds, Cambridge University Press, Cambridge, 1982
[11] M. Emery, Stochastic Calculus on Manifolds, Springer, Berlin, 1989
[12] M. I. Freidlin, “On factorization of positive semi-definite matrices”, Probability Theory and Its Applications, 13:2 (1968), 375–378
[13] Yu. E. Gliklikh, Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics, Kluwer, Dordrecht, 1996
[14] Yu. E. Gliklikh, Global Analysis in Mathematical Physics. Geometric and Stochastic Methods, Springer, New York, 1997
[15] Yu. E. Gliklikh, Global and Stochastic Analysis in Problems of Mathematical Physics, KomKniga, Moscow, 2005 (in Russian)
[16] Yu. E. Gliklikh, “Stochastic differential inclusions with mean derivatives on non-compact manifolds”, Seminar on global and stochastic analysis, Voronezh University, 2008, no. 3, 12–30
[17] Yu. E. Gliklikh, “On relations between infinitesimal generators and mean derivatives of stochastic processes on manifolds”, Proceedings of Voronezh State University, Series Physics Mathematics, 2008, no. 2, 97–102
[18] X. He, “A probabilistic method for Navier–Stokes vorticies”, J. Appl. Probab., 2001, 1059–1066
[19] P. A. Meyer, “A differential geometric formalism for the Itô calculus”, Lecture Notes in Mathematics, 851, 1981, 256–270
[20] E. Nelson, “Derivation of the Schrödinger equation from Newtonian mechanics”, Phys. Rev., 150:4 (1966), 1079–1085
[21] E. Nelson, Dynamical Theory of Brownian Motion, Princeton Univ. Press, Princeton, 1967
[22] E. Nelson, Quantum Fluctuations, Princeton Univ. Press, Princeton, 1985
[23] L. Schwartz, Semimartingales and Their Stochastic Calculus on Manifolds, Montreal University Press, Montreal, 1984