Geodesic
Distribution of functionals of certain non-Markovian processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 481-505

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We examine the problem of computation of the functionals of a non-Markovian process of a special kind. We establish that, for such functionals, the moment generating function is a solution of a family of differential problems with unusual conditions on the jump of the derivative. That solution is proved to be unique, and its general form is determined and examples of computation of the distribution of specific functionals are given.
Keywords: distribution of a functional, Brownian motion, Brownian local time. 
@article{TVP_1999_44_3_a0,
     author = {A. N. Borodin},
     title = {Distribution of functionals of certain {non-Markovian} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {481--505},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a0/}
}
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A. N. Borodin. Distribution of functionals of certain non-Markovian processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 481-505. http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a0/