Discussiones Mathematicae Differential Inclusions 17 (1997) 107-131

[BIBTex]

EXISTENCE OF VIABLE SOLUTIONS FOR A NONCONVEX STOCHASTIC DIFFERENTIAL INCLUSION

Benoit Truong-Van

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

Truong Xuan Duc Ha

Hanoi Institute of Mathematics
P.O. Box 631, Boho, Hanoi, Vietnam

Abstract

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.

Keywords: Stochastic differential inclusion, viable solution, tangential condition, Lipschitz property.

1991 Mathematics Subject Classifications: 60H10, 34A60.

References

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Received 15 December 1997
Revised 19 March 1998