A non-stationary ergodic theorem with applications to averaging – Bob Pepin

Bob Pepin
University of Luxembourg

Date(s) : 26/01/2018   iCal
11 h 00 min - 12 h 00 min

The $L^2$ distance between an additive functional of a Markov diffusion process and its expectation is expressed in terms of the gradient of the semigroup or evolution operator. The result holds without any stationarity assumptions and in particular for SDEs with time-dependent coefficients. As an application, we compute the exact expression for the $L^2$ distance between a linear SDE with two time scales and the corresponding time-averaged process. The proof of the ergodic theorem is based on a short martingale argument that readily extends to pathwise estimates and other classes of stochastic processes.



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