Existence of viable solutions for a nonconvex stochastic differential inclusion

• Autorzy: Benoit Truong-Van , Truong Xuan Duc Ha
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Stochastic differential inclusion; viable solution; tangential condition; Lipschitz property

Kategorie tematyczne

• 60H10: Stochastic ordinary differential equations
• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1997
• Tom: 17
• Numer: 1-2
• Strony: 107-131

Daty

wydano

1997

otrzymano

1997-12-15

poprawiono

1998-03-19

Twórcy

autor

Benoit Truong-Van

• Laboratoire de Mathématiques Appliquées, URA-CNRS 1204 Université de Pau, France

autor

Truong Xuan Duc Ha

• 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.