Electronic Communications in Probability

Variably Skewed Brownian Motion

Martin Barlow, Krzysztof Burdzy, Haya Kaspi, and Avi Mandelbaum

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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.

Article information

Source
Electron. Commun. Probab., Volume 5 (2000), paper no. 6, 57-66.

Dates
Accepted: 1 March 2000
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456943499

Digital Object Identifier
doi:10.1214/ECP.v5-1018

Mathematical Reviews number (MathSciNet)
MR1752008

Zentralblatt MATH identifier
0949.60090

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Skew Brownian motion Brownian motion stochastic differential equation local time

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Barlow, Martin; Burdzy, Krzysztof; Kaspi, Haya; Mandelbaum, Avi. Variably Skewed Brownian Motion. Electron. Commun. Probab. 5 (2000), paper no. 6, 57--66. doi:10.1214/ECP.v5-1018. https://projecteuclid.org/euclid.ecp/1456943499


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