Related papers: Stochastic systems with memory and jumps

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…

Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and…

This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a…

Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…

We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations,…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…

This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…

The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…

We develop a prototypical stochastic model for local search around a given home. The stochastic dynamic model is motivated by experimental findings of the motion of a fruit fly around a given spot of food but shall generally describe local…

A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…

We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which…