Invariant measures related with Poisson driven stochastic differential equation

Andrzej Lasota and Janusz Traple

Stochastic Processes and their Applications, 2003, vol. 106, issue 1, 81-93

Abstract: A Poisson driven stochastic differential equation generates a semigroup of operators (Pt)t[greater-or-equal, slanted]0 describing the evolution of measures along trajectories and a Markov operator P corresponding to the change of measures from a jump to jump. We show that the semigroup (Pt)t[greater-or-equal, slanted]0 has a finite invariant measure if and only if the operator P has the same property. The main result is applied to problems related with the existence and the dimension of invariant measures.

Keywords: Stochastic; differential; equation; Invariant; measure; Markov; operator; Semigroup; of; linear; operators; Hausdorff; dimension (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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