We study the existence of strong solutions for a class of stochastic differential equations in an infinite dimensional space. Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in time of the stochastic perturbation. This leads to an abstract formulation in terms of a stochastic diffusion with dynamic boundary conditions, featuring fractional Brownian motion. We prove results on existence, uniqueness and asymptotics of weak and strong solutions to such a stochastic differential equation.

Existence of strong solutions for neuronal network dynamics driven by fractional Brownian motions

Bonaccorsi, Stefano;Mugnolo, Delio
2010-01-01

Abstract

We study the existence of strong solutions for a class of stochastic differential equations in an infinite dimensional space. Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in time of the stochastic perturbation. This leads to an abstract formulation in terms of a stochastic diffusion with dynamic boundary conditions, featuring fractional Brownian motion. We prove results on existence, uniqueness and asymptotics of weak and strong solutions to such a stochastic differential equation.
2010
3
Bonaccorsi, Stefano; Mugnolo, Delio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/84385
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