Abstract. We study existence and uniqueness of an invariant measure for infinite dimensional stochastic differential equations with dissipative polynomially bounded nonlinear terms. We also exhibit the existence of a density with respect to a Gaussian measure. Moreover, we decompose the solution process into a stationary component and a component which vanishes asymptotically in the L 2 -sense. Applications are given to neurobiological networks where the signals propagation is modelled by a system of coupled stochastic FitzHugh-Nagumo equations.

Invariant measures for stochastic differential equations on networks

DI PERSIO, Luca;
2013

Abstract

Abstract. We study existence and uniqueness of an invariant measure for infinite dimensional stochastic differential equations with dissipative polynomially bounded nonlinear terms. We also exhibit the existence of a density with respect to a Gaussian measure. Moreover, we decompose the solution process into a stationary component and a component which vanishes asymptotically in the L 2 -sense. Applications are given to neurobiological networks where the signals propagation is modelled by a system of coupled stochastic FitzHugh-Nagumo equations.
9780821875742
Invariant measures; infinite dimensional stochastic differential equations; dissipative systems; neurobiological networks; stochastic FitzHugh-Nagumo systems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/744564
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