MEASURE EVOLUTION FOR 'STOCHASTIC FLOWS'

摘要

In this paper we study how σ-finite measures on R{sup}d evolve under a class of "stochastic flows" associated to stochastic differential equations with (resp. without) jumps in R{sup}d. First we show the related measure evolution processes are cadlag (resp. continuous), strongly Markovian and weakly Fellerian. Then we extend the existing results on incompressibility in Harris [8] and Kunita [14], and prove strong Markov property of the process describing how compact subsets evolve under incompressible "stochastic flows" under a certain condition.