Related papers: Analysis and Approximation of Stochastic Nerve Axo…
This paper deals with the existence and limiting behavior of invariant measures of the stochastic Landau-Lifshitz-Bloch equation driven by linear multiplicative noise and additive noise defined in the entire space $\mathbb{R}^d$ for…
Many modern applications of the artificial neural networks ensue large number of layers making traditional digital implementations increasingly complex. Optical neural networks offer parallel processing at high bandwidth, but have the…
A standard finite element method discretizes the stochastic linear Schr\"{o}dinger equation driven by additive noise in the spatial variables. The weak convergence of the resulting approximate solution is analyzed, and it is established…
We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
This paper proposes and analyzes a novel fully discrete finite element scheme with the interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-side Lipschitz condition and…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…
We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two…
We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the…
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…
In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\gg 1$ stochastic delay-differential equations is derived. The resulting…
The ability to quantify stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally…