Path transformations for local times of one-dimensional diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Cetin, Umut¹ 

[1] London Sch Econ & Polit Sci, Dept Stat, 10 Houghton St, London WC2A 2AE, England

关键词: Regular one-dimensional diffusions;    Local time;    Engelbert-Schmidt theory of weak solutions;    Bessel processes;    Time reversal;    Path decomposition of Markov processes;   

DOI  :  10.1016/j.spa.2017.11.005

来源: Elsevier

【 摘 要 】

Let X be a regular one-dimensional transient diffusion and L-y be its local time at y. The stochastic differential equation (SDE) whose solution corresponds to the process X conditioned on [L-infinity(y) = a] for a given a >= 0 is constructed and a new path decomposition result for transient diffusions is given. In the course of the construction Bessel-type motions as well as their SDE representations are studied. Moreover, the Engelbert-Schmidt theory for the weak solutions of one dimensional SDEs is extended to the case when the initial condition is an entrance boundary for the diffusion. This extension was necessary for the construction of the Bessel-type motion which played an essential part in the SDE representation of X conditioned on [L-infinity(y) = a]. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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