Given a Lipschitz continuous multifunction F on (Formula presented.) , we construct a probability measure on the set of all solutions to the Cauchy problem (Formula presented.) with x(0) = 0. With probability one, the derivatives of these random solutions take values within the set extF(x) of extreme points for a.e. time t. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.
All Science Journal Classification (ASJC) codes
- Applied Mathematics