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Variably Skewed Brownian Motion

   
@article{ECP1018,
	author = {Martin Barlow and Krzysztof Burdzy and Haya Kaspi and Avi Mandelbaum},
	title = {Variably Skewed Brownian Motion},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {5},
	year = {2000},
	keywords = {Skew Brownian motion, Brownian motion, stochastic differential equation,local time},
	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.},
	pages = {no. 6, 57-66},
	issn = {1083-589X},
	doi = {10.1214/ECP.v5-1018},    
        url = {http://ecp.ejpecp.org/article/view/1018}}