Variably Skewed Brownian Motion

Martin Barlow, Krzysztof Burdzy, Haya Kaspi, Avi Mandelbaum
2000 Electronic Communications in Probability  
Given a standard Brownian motion B, we show that the equation has a unique strong solution X. Here L X is the symmetric local time of X at 0, and β is a given differentiable function with β(0) = 0, −1 < β (·) < 1. (For linear β(·), the solution is the familiar skew Brownian motion).
doi:10.1214/ecp.v5-1018 fatcat:aaeixuxhz5bc3p5blpdwgo4doa