منابع مشابه
On Skew Brownian Motion
We consider the stochastic equation X(t) = W(t) + βlX0(t), where W is a standard Wiener process and lX0(⋅) 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 |β| ≤ 1, but no solutions exist if |β| > 1. In the former case, setting α = (β + 1)/2, the unique solution X is distributed as a skew Brownian motion with parameter α....
متن کاملIs a Brownian motion skew?
Abstract: We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the Skew Brownian motion being a...
متن کاملFirst Passage Time of Skew Brownian Motion
Nearly fifty years after the introduction of skew Brownian motion by Itô and McKean (1963), the first passage time distribution remains unknown. In this paper, we first generalize results of Pitman and Yor (2001) and Csáki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion, and then use this result to derive the first passage time distribut...
متن کاملOn the constructions of the skew Brownian motion
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with a brief account of related results, extensions and applications of the Skew Brownian motion. AMS 2000 subject classifications: Primary 60J60; secondary 60H1...
متن کاملLocal Time Flow Related to Skew Brownian Motion
We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the RayKnight theorem on local times. In our case, however, t...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1981
ISSN: 0091-1798
DOI: 10.1214/aop/1176994472