Geodesic
Estimation of the evolution of a random set
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 14-25

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An estimation problem for a random set that is a reachability domain of the Ito differential equation with respect to its initial data is considered. The Markov property of the reachability 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.
Keywords: stochastic differential equation, random set.
Mots-clés : Markov chain 
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     author = {B. I. Anan'ev},
     title = {Estimation of the evolution of a random set},
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B. I. Anan'ev. Estimation of the evolution of a random set. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 14-25. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a1/