Invariant measures related with randomly connected Poisson driven differential equations

Katarzyna 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 -