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Averaging dynamics driven by fractional Brownian motion

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1902.11251v1.pdfWorking paper418.88 kBAdobe PDFView/Open
Title: Averaging dynamics driven by fractional Brownian motion
Authors: Hairer, M
Li, X-M
Item Type: Working Paper
Abstract: We consider slow / fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter $H>{1\over 2}$. We show that unlike in the case $H={1\over 2}$, convergence to the averaged solution takes place in probability and the limiting process solves the 'na\"ively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.
Issue Date: 28-Feb-2019
URI: http://hdl.handle.net/10044/1/72214
Keywords: math.PR
math.PR
60G22, 60H10, 60H05
math.PR
math.PR
60G22, 60H10, 60H05
Appears in Collections:Pure Mathematics
Mathematics



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