Related papers: Statistical determinism in non-Lipschitz dynamical…

A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…

We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…

In this paper, we introduce regularized stochastic team problems. Under mild assumptions, we prove that there exists an unique fixed point of the best response operator, where this unique fixed point is the optimal regularized team decision…

Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…

Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players'…

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a…

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…

We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

The article is dedicated to discussion of irreversibility and foundation of statistical mechanics "from the first principles". Taking into account infinitesimal and, as it seems, neglectful for classical mechanics fluctuations of the…

We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…

This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…

In this paper, we study the existence of random periodic solutions for nonlinear stochastic differential equations with additive white noise. We extend the input-to-state characteristic operator of the system to the non-autonomous…

A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which…

We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…