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Type: Artigo
Title: Decomposition Of Stochastic Flows Generated By Stratonovich Sdes With Jumps
Author: Melo
Alison M.; Morgado
Leandro B.; Ruffino
Paulo R.
Abstract: Consider a manifold M endowed locally with a pair of complementary distributions Delta(H) (R) Delta(V) = TM and let Diff(Delta(H), M) and Diff(Delta(V), M) be the corresponding Lie subgroups generated by vector fields in the corresponding distributions. We decompose a stochastic flow with jumps, up to a stopping time, as phi(t) = xi(t) o psi(t), where xi(t) is an element of Diff(Delta(H), M) and psi(t) is an element of Diff(Delta(V), M). Our main result provides Stratonovich stochastic differential equations with jumps for each of these two components in the corresponding infinite dimensional Lie groups. We present an extension of the It (o) over cap -Ventzel-Kunita formula for stochastic flows with jumps generated by classical Marcus equation (as in Kurtz, Pardoux and Protter [11]). The results here correspond to an extension of Catuogno, da Silva and Ruffino [4], where this decomposition was studied for the continuous case.
Editor: Amer Inst Mathematical Sciences-Aims
Citation: Discrete And Continuos Dynamical Systems-series B. Amer Inst Mathematical Sciences-aims, v. 21, p. 3209 - 3218, 2016.
Rights: fechado
Identifier DOI: 10.3934/dcdsb.2016094
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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