# Invariant measures related with randomly connected Poisson driven differential equations

Annales Polonici Mathematici (2002)

- Volume: 79, Issue: 1, page 31-44
- ISSN: 0066-2216

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topKatarzyna Horbacz. "Invariant measures related with randomly connected Poisson driven differential equations." Annales Polonici Mathematici 79.1 (2002): 31-44. <http://eudml.org/doc/280654>.

@article{KatarzynaHorbacz2002,

abstract = {We consider the stochastic differential equation
(1) $du(t) = a(u(t),ξ(t))dt + ∫_\{Θ\} σ(u(t),θ) _p(dt,dθ)$ for t ≥ 0
with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup $\{P^t\}_\{t≥0\}$ 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 $\{P^t\}_\{t≥0\}$ describing the evolution of measures along trajectories and vice versa.},

author = {Katarzyna Horbacz},

journal = {Annales Polonici Mathematici},

keywords = {stochastic differential equation with Poisson type perturbations; existence of invariant measure; Poisson random counting measure; Markov semigroup; Markov chains; Markov operators; Feller operator; Lévy concentration function; Hausdorff dimension; generalized Rényi dimensions},

language = {eng},

number = {1},

pages = {31-44},

title = {Invariant measures related with randomly connected Poisson driven differential equations},

url = {http://eudml.org/doc/280654},

volume = {79},

year = {2002},

}

TY - JOUR

AU - Katarzyna Horbacz

TI - Invariant measures related with randomly connected Poisson driven differential equations

JO - Annales Polonici Mathematici

PY - 2002

VL - 79

IS - 1

SP - 31

EP - 44

AB - We consider the stochastic differential equation
(1) $du(t) = a(u(t),ξ(t))dt + ∫_{Θ} σ(u(t),θ) _p(dt,dθ)$ for t ≥ 0
with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup ${P^t}_{t≥0}$ 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 ${P^t}_{t≥0}$ describing the evolution of measures along trajectories and vice versa.

LA - eng

KW - stochastic differential equation with Poisson type perturbations; existence of invariant measure; Poisson random counting measure; Markov semigroup; Markov chains; Markov operators; Feller operator; Lévy concentration function; Hausdorff dimension; generalized Rényi dimensions

UR - http://eudml.org/doc/280654

ER -

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