Finitely Approximable Random Sets and their Evolution via Differential Equations.

In this paper, random closed sets (RCS) in Euclidean space are considered along with their distributions and approximation. Distributions of RCS may be used for the calculation of expectation and other characteristics. Reachable sets on initial data and some ways of their approximate evolutionary description are investigated for stochastic differential equations (SDE) with initial state in some RCS. Markov property of random reachable sets is proved in the space of closed sets. For approximate calculus, the initial RCS is replaced by a finite set on the integer multidimensional grid and the multistage Markov chain is substituted for SDE. The Markov chain is constructed by methods of SDE numerical integration. Some examples are also given. [ABSTRACT FROM AUTHOR]