Discussiones Mathematicae Differential Inclusions 17 (1997) 107131
Benoit TruongVan Laboratoire de Mathématiques Appliquées 
Truong Xuan Duc Ha Hanoi Institute of Mathematics 
For the stochastic viability problem of the form

where K, F are setvalued maps which may have nonconvex values, g is a singlevalued 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.
[1]  J.P. Aubin, G. Da Prato, Stochastic viability and invariance, Annali Scuola Normale di Pisa, 27 (1990), 595614. 
[2]  J.P. Aubin, G. Da Prato, Stochastic Nagumo's viability theorem, Stochastic Analysis and Applications, 13 (1995), 111. 
[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), 13951414. 
[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), 6174. 
[7]  A. Milian, A note on the stochastic invariance for Itô equations, Bulletin of the Polish Academy of Sciences Mathematics, 41 (1993), 139150. 
[8]  X.D.H. Truong, Existence of viable solutions of nonconvexvalued differential inclusions in Banach spaces, Portugalae Mathematica, 52 (1995), 241250. 
[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), 213236. 
Received 15 December 1997
Revised 19 March 1998