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Trivariate density of Brownian motion, its local and occupation times, with application to stochastic control. (English) Zbl 0544.60069
Using the Feynman-Kac formula and Laplace transform the authors compute the joint density of Brownian motion, its local time at the origin, and its occupation time of $$[0,\infty)$$, with zero and nonzero initial condition. From these results and the Girsanov transformation the transition probabilities of a Brownian motion whose drift switches between two values as the process crosses a threshold is obtained.
Reviewer: A.D.Borisenko

##### MSC:
 60J65 Brownian motion 93E20 Optimal stochastic control 60G17 Sample path properties
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