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1997 | 17 | 1-2 | 107-131
Tytuł artykułu

Existence of viable solutions for a nonconvex stochastic differential inclusion

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EN
For the stochastic viability problem of the form
dx(t) ∈ F(t,x(t))dt+g(t,x(t))dW(t), x(t) ∈ K(t),
where K, F are set-valued maps which may have nonconvex values, g is a single-valued function, we establish the existence of solutions under the assumption that F and g possess Lipschitz property and satisfy some tangential conditions.
Twórcy
  • Laboratoire de Mathématiques Appliquées, URA-CNRS 1204 Université de Pau, France
  • Hanoi Institute of Mathematics, P.O. Box 631, Boho, Hanoi, Vietnam
Bibliografia
  • [1] J.P. Aubin, G. Da Prato, Stochastic viability and invariance, Annali Scuola Normale di Pisa, 27 (1990), 595-614.
  • [2] J.P. Aubin, G. Da Prato, Stochastic Nagumo's viability theorem, Stochastic Analysis and Applications, 13 (1995), 1-11.
  • [3] N. Dunford, J.T. Schwartz, Linear Operators, Part I, Interscience Publisher Inc., New York 1957.
  • [4] S. Gautier, L.Thibault, Viability for constrained stochastic differential equations, Differential and Integral Equations 6 (6) (1993), 1395-1414.
  • [5] I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer Verlag, New York 1988.
  • [6] M. Kisielewicz, Viability theorem for stochastic inclusions, Discussiones Mathematicae - Differential Inclusions 15 (1995), 61-74.
  • [7] A. Milian, A note on the stochastic invariance for Itô equations, Bulletin of the Polish Academy of Sciences Mathematics, 41 (1993), 139-150.
  • [8] X.D.H. Truong, Existence of viable solutions of nonconvex-valued differential inclusions in Banach spaces, Portugalae Mathematica, 52 (1995), 241-250.
  • [9] X.D.H. Truong, An existence result for nonconvex viability problem in Banach spaces, Preprint N.16 (1996), University of Pau, France.
  • [10] Qi Ji Zhu, On the solution set of differential inclusions in Banach spaces, J. Differential Equations, 93 (2) (1991), 213-236.
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