Related papers: Stochastic Maps, Continuous Approximation and Stab…
We present an efficient and validated method for approximating the stationary measures of random dynamical systems with smooth additive noise. The approach leverages the strong regularizing properties of the associated transfer operator…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…
Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with Stratonovich noise on the one dimensional torus. As a main result we show the continuity of the…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely path. Any density peak moves along such a…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…
A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point…
Stochastic learning dynamics based on Langevin or Levy stochastic differential equations (SDEs) in deep neural networks control the variance of noise by varying the size of the mini-batch or directly those of injecting noise. Since the…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…