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

@inproceedings{Faggionato2022AMA, title={A martingale approach to time-dependent and time-periodic linear response in Markov jump processes}, author={Alessandra Faggionato and Vittoria Silvestri}, year={2022} }

. 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…

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