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- W2000991167 abstract "We consider the stochastic equation $X(t) = W(t) + beta l^X_0(t)$, where $W$ is a standard Wiener process and $l^X_0(cdot)$ is the local time at zero of the unknown process $X$. There is a unique solution $X$ (and it is adapted to the fields of $W$) if $|beta| leq 1$, but no solutions exist if $|beta| > 1$. In the former case, setting $alpha = (beta + 1)/2$, the unique solution $X$ is distributed as a skew Brownian motion with parameter $alpha$. This is a diffusion obtained from standard Wiener process by independently altering the signs of the excursions away from zero, each excursion being positive with probability $alpha$ and negative with probability $1 - alpha$. Finally, we show that skew Brownian motion is the weak limit (as $n rightarrow infty$) of $n^{-1/2}S_{lbrack ntrbrack}$, where $S_n$ is a random walk with exceptional behavior at the origin." @default.
- W2000991167 created "2016-06-24" @default.
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- W2000991167 date "1981-04-01" @default.
- W2000991167 modified "2023-10-13" @default.
- W2000991167 title "On Skew Brownian Motion" @default.
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- W2000991167 doi "https://doi.org/10.1214/aop/1176994472" @default.
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