Geodesic
On a probabilistic method of solving a one-dimensional initial-boundary value problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 255-281

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We obtain an analogue of probabilistic representation of a solution of an initial-boundary value problem for the equation $\partial u/\partial t+(\sigma^2/2)\partial^2u/\partial x^2+f(x)u=0$, where $\sigma$ is a complex number.
Keywords: random processes; evolution equation; limit theorems; Feynman–Kac formula; Feynman integral; Feynman measure. 
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     title = {On a probabilistic method of solving a one-dimensional initial-boundary value problem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a3/}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. On a probabilistic method of solving a one-dimensional initial-boundary value problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 255-281. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a3/