Abstract:
A description of the local time of the reflecting Brownian motion as a process with respect to the spatial variable is given. It turns out that such a process is Markovian if instead of a non-random time we substitute an exponentially distributed time independent of the process. We are interested in the result that allows us to calculate the distributions of integral functionals with respect to the spatial variable of the local time of reflecting Brownian motion. The explicit distribution of the supremum of the local time with respect to the spatial variable is calculated.
Key words and phrases:of reflecting Brownian motion, local time, distribution of the supremum of local time.
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