Variably Skewed Brownian Motion

Martin Barlow (University of British Columbia)
Krzysztof Burdzy (University of Washington)
Haya Kaspi (Technion Institute)
Avi Mandelbaum (Technion Institute)

Abstract


Given a standard Brownian motion $B$, we show that the equation $$ X_t = x_0 + B_t + \beta(L_t^X), t \geq 0,$$ has a unique strong solution $X$. Here $L^X$ is the symmetric local time of $X$ at $0$, and $\beta$ is a given differentiable function with $\beta(0) = 0$, whose derivative is always in $(-1,1)$. For a linear function $\beta$, the solution is the familiar skew Brownian motion.

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Pages: 57-66

Publication Date: March 1, 2000

DOI: 10.1214/ECP.v5-1018

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