Splitting: Tanaka's SDE revisited

1999/11/16 by Jon warren, warren, Jon
Mathematics · #60G20 (Primary) 60J65 #60H20 (Secondary) #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G20 #msc:60H20 #msc:60J65

paper · pdf · doi:10.48550/arxiv.math/9911115

6 pages, LaTex2e

arxiv created 1999/11/16 · arxiv updated 2009/11/30

Abstract

The weak solution of Tanaka's SDE is not a function of the driving Brownian motion, and therefore it has no Wiener chaos expansion. However in some sense explained here it has a generalised chaos expansion involving infinite products of stochastic differentials accumulating at the minimum of the Brownian path. This is related to the existence of a non-classical noise richer than the usual white noise.

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