In our paper, we construct an analog of probabilistic representation of the solution of the Cauchy problem for the equation \( \frac{{\partial u}}{{\partial t}}+\frac{{{\sigma^2}}}{2}\frac{{{\partial^2}u}}{{\partial {x^2}}}+f(x)u=0, \) where σ is a complex number. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 396, 2012, pp. 111–143.
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Ibragimov, I.A., Smorodina, N.V. & Faddeev, M.M. Probabilistic approximation of solutions of the cauchy problem for some evolution equations. J Math Sci 188, 700–716 (2013). https://doi.org/10.1007/s10958-013-1161-8
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DOI: https://doi.org/10.1007/s10958-013-1161-8