• Corpus ID: 245837825

A martingale approach to time-dependent and time-periodic linear response in Markov jump processes

  title={A martingale approach to time-dependent and time-periodic linear response in Markov jump processes},
  author={Alessandra Faggionato and Vittoria Silvestri},
. We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the perturbation we show that the perturbed process does not explode almost surely and we study the linear response (LR) of observables and additive functionals. When the unperturbed process is stationary, the above LR formulas become computable in terms of the steady… 



Limit theorems for stochastic processes (Vol. 288)

  • Springer Science & Business Media
  • 2013

Piecewise-deterministic Markov Processes: A General Class of Non-diffusion Stochastic Models

Stochastic calculus for these stochastic processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper.

Response Theory: A Trajectory-Based Approach

  • C. Maes
  • Physics
    Frontiers in Physics
  • 2020
We collect recent results on deriving useful response relations also for non-equilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space.

Steady States, Fluctuation–Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe

Markov Models and Optimization

Analysis, probability and stochastic processes piecewise deterministic processes expectations and distributions control theory control by intervention.

The technique of the exponential change of measure for Markov processes

It is demonstrated that the process X (t) is a Markov process on the probability space (U, F, fF tg, ~ P), and the extended generator ~ A is found and provided sufficient conditions under which D(~ A) 1⁄4 D(A).

A Short Introduction to Perturbation Theory for Linear Operators

Method of Lyapunov functions for analysis of absorption and explosion in Markov chains

Several theorems concerned with sufficient conditions for testing the absorption, explosion, and nonexplosion of time-inhomogeneous Markov chains with a countable state space are proved for a general class of Markov Chains.