Long-time behavior of stochastically perturbed neuronal networks

Abstract

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.

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Cited by in corpus (4)

• On the stochastic Allen-Cahn equation on networks with multiplicative noise
• Stochastic reaction-diffusion equations on networks
• Absolute continuity of the law for solutions of stochastic differential equations with boundary noise
• On the parabolic Cauchy problem for quantum graphs with vertex noise