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2001 | 21 | 2 | 173-190
Tytuł artykułu

Stochastic differential inclusions of Langevin type on Riemannian manifolds

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EN
Abstrakty
EN
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
Twórcy
  • Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394693, Voronezh, Russia
  • Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394693, Voronezh, Russia
Bibliografia
  • [1] P. Billingsley, Convergence of Probability Measures, New York et al., Wiley 1969.
  • [2] R.L. Bishop and R.J. Crittenden, Geometry of Manifolds, New York-London, Academic Press 1964.
  • [3] Yu.G. Borisovich and Yu.E. Gliklikh, On Lefschetz number for a certain class of set-valued maps, 7-th Summer Mathematical School., Kiev (1970), 283-294 (in Russian).
  • [4] E.D. Conway, Stochastic equations with discontinuous drift, Trans. Amer. Math. Soc. 157 (1) (1971), 235-245.
  • [5] I.I. Gihman and A.V. Skorohod, Theory of Stochastic Processes 1, New York, Springer-Verlag 1979.
  • [6] I.I. Gihman and A.V. Skorohod, Theory of Stochastic Processes 3, New York, Springer-Verlag 1979.
  • [7] Yu.E. Gliklikh, Fixed points of multivalued mappings with nonconvex images and the rotation of multivalued vector fields, Sbornik Trudov Aspirantov Matematicheskogo Fakul'teta, Voronezh University (1972), 30-38 (in Russian).
  • [8] Yu.E. Gliklikh and I.V. Fedorenko, On the geometrization of a certain class of mechanical systems with random perturbations of the force, Voronezh University, Deposited in VINITI, October 21, 1980, N 4481 (in Russian).
  • [9] Yu.E. Gliklikh and I.V. Fedorenko, Equations of geometric mechanics with random force fields, Priblizhennye metody issledovaniya differentsial'nykh uravneni i ikh prilozheniya, Kubyshev 1981, 64-72 (in Russian).
  • [10] Yu.E. Gliklikh, Riemannian parallel translation in non-linear mechanics, Lect. Notes Math. 1108 (1984), 128-151.
  • [11] Yu.E. Gliklikh, Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics, Dordrecht, Kluwer 1996, xvi+189.
  • [12] Yu.E. Gliklikh, Global Analysis in Mathematical Physics, Geometric and Stochastic Methods, New York, Springer-Verlag 1997, xv+213.
  • [13] A.N. Kolmogorov and S.V. Fomin, Elements of theory of functions and functional analysis, Moscow, Nauka 1968.
  • [14] W. Kryszewski, Homotopy properties of set-valued mappings, Toruń, Toruń University 1997, 243.
  • [15] J. Motyl, On the Solution of Stochastic Differential Inclusion, J. Math. Anal. and Appl. 192 (1995), 117-132.
  • [16] A.D. Myshkis, Generalization of the theorem on the stationary point of the dynamical system inside a closed trajectory, Mat. Sbornik 34 (3) (1954), 525-540.
  • [17] K.R. Parthasarathy, Introduction to Probability and Measure, New York, Springer-Verlag 1978.
  • [18] A.N. Shiryaev, Probability, Moscow, Nauka 1989.
  • [19] Y. Yosida, Functional Analysis, Berlin et. al., Springer-Verlag 1965.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1023
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