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Variably Skewed Brownian Motion
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Martin Barlow, University of British Columbia
Krzysztof Burdzy, University of Washington
Haya Kaspi, Technion Institute
Avi Mandelbaum, Technion Institute
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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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Full text: PDF
Pages: 57-66
Published on: March 1, 2000
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Electronic Communications in Probability. ISSN: 1083-589X |
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