Invariant measures related with randomly connected Poisson driven differential equations

• Autorzy: Katarzyna Horbacz
• Języki publikacji: EN

Abstrakty

EN

We consider the stochastic differential equation
(1) $du(t) = a(u(t),ξ(t))dt + ∫_{Θ} σ(u(t),θ) 𝓝_p(dt,dθ)$ 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.

Kategorie tematyczne

• 34F05: Equations and systems with randomness
• 37C45: Dimension theory of dynamical systems
• 60J25: Continuous-time Markov processes on general state spaces
• 60H10: Stochastic ordinary differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 79
• Numer: 1
• Strony: 31-44

Daty

wydano

2002

Twórcy

autor

Katarzyna Horbacz

• Institute of Mathematics, Silesian University, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/ap79-1-3