A New Class of Theorems of the Alternative |
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| Authors: | A I Golikov Yu G Evtushenko |
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| Institution: | 1.Ural Federal University,Yekaterinburg,Russia;2.Krasovskii Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia |
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| Abstract: | An estimation problem for a random set that is a reachable domain of the Ito differential equation with respect to its initial data is considered. The Markov property of the reachable set in the space of closed sets is proved. For the purposes of numerical solution, a random initial set of the differential equation is approximated by a finite set on an integer multidimensional grid, and the differential equation is replaced by a multistep Markov chain. Examples are considered. |
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