Geodesic
A probabilistic approximation of the Cauchy problem solution of some evolution equations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 111-143

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In our paper we construct an analogy of a probabilistic representation of the Cauchy problem solution of the equation $\frac{\partial u}{\partial t}+\frac{\sigma^2}2\frac{\partial^2u}{\partial x^2}+f(x)u=0$, where $\sigma$ is a complex number. 
@article{ZNSL_2011_396_a7,
     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {A probabilistic approximation of the {Cauchy} problem solution of some evolution equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {111--143},
     publisher = {mathdoc},
     volume = {396},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a7/}
}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. A probabilistic approximation of the Cauchy problem solution of some evolution equations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 111-143. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a7/