Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Locally stationary random processes

Abstract: A new kind of random process, the locally stationary random process, is defined, which includes the stationary random process as a special case. Numerous examples of locally stationary random processes are exhibited. By the generalized spectral density \Psi(\omega, \omega \prime) of a random process is meant the two-dimensional Fourier transform of the covariance of the process; as is well known, in the case of stationary processes, \Psi(\omega, \omega \prime) reduces to a positive mass distribution on the line \omega = \omega \prime in the \omega, \omega \prime plane, a fact which is the gist of the familiar Wiener-Khintchine relations. In the case of locally stationary random processes, a relation is found between the covariance and the spectral density which constitutes a natural generalization of the Wiener-Khintchine relations.

Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays.

Abstract: We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L'Heureux, and Longtin. We derive an analytical expression for stationary distributions using first-order perturbation theory. We demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data. In addition, we show that the Fokker-Planck perspective for stochastic systems with time delays is consistent with the so-called extended phase-space approach to time-delayed systems.

Fast Distributed Algorithms for Computing Separable Functions

Abstract: The problem of computing functions of values at the nodes in a network in a fully distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad hoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend, in general, to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete fully distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme.

A Contraction Theory Approach to Stochastic Incremental Stability

Abstract: We investigate the incremental stability properties of Ito stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of nonlinear observers design and stochastic synchronization.