A non-stationary ergodic theorem with applications to averaging – Bob Pepin
Bob Pepin
University of Luxembourg
https://www.researchgate.net/scientific-contributions/Bob-Pepin-2132962653
Date(s) : 26/01/2018 iCal
11h00 - 12h00
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.
http://wwwfr.uni.lu/recherche/fstc/mathematics_research_unit/people/bob_pepin
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