The paper deals with some problems concerning probabilistic representation and probabilistic approximation for solution of the Cauchy problem for the family of equations \( \frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\varDelta u \) with complex parameter σ such that Reσ 2 ≥ 0. This family coincides with the heat equation if Imσ = 0, and with the Schrӧdinger equation if Reσ 2 = 0. Bibliography: 5 titles
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 242–252.
Translated by I. Ponomarenko.
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Tsykin, S.V. On an Approximation for the Solutions of Some Evolution Equations by the Expectations of Random Walks Functionals. J Math Sci 214, 584–591 (2016). https://doi.org/10.1007/s10958-016-2800-7
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DOI: https://doi.org/10.1007/s10958-016-2800-7