Invariant measures related with randomly connected Poisson driven differential equations

Katarzyna Horbacz

Annales Polonici Mathematici, Tome 79 (2002), p. 31-44 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the stochastic differential equation (1) $d u (t) = a (u (t), ξ (t)) d t + \int_{Θ} σ {(u (t), θ)}_{p} (d t, d θ)$ for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup ${P^{t}}_{t \geq 0}$ corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup ${P^{t}}_{t \geq 0}$ describing the evolution of measures along trajectories and vice versa.

Publié le : 2002-01-01

Zbl 1011.60036

EUDML-ID : urn:eudml:doc:280654

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     author = {Katarzyna Horbacz},
     title = {Invariant measures related with randomly connected Poisson driven differential equations},
     journal = {Annales Polonici Mathematici},
     volume = {79},
     year = {2002},
     pages = {31-44},
     zbl = {1011.60036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-1-3}
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Katarzyna Horbacz. Invariant measures related with randomly connected Poisson driven differential equations. Annales Polonici Mathematici, Tome 79 (2002) pp. 31-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-1-3/