The paper is devoted to some problems associated with a probabilistic representation and probabilistic approximation of the Cauchy problem solution for the family of equations \( \frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\varDelta u \) with a complex parameter σ such that Re σ2 ≥ 0. The above family includes as a particular case both the heat equation (Im σ = 0) and the Schrödinger equation (Re σ2 = 0).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 420, 2013, pp. 88–102.
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Ibragimov, I.A., Smorodina, N.V. & Faddeev, M.M. A Limit Theorem on the Convergence of Random Walk Functionals to a Solution of the Cauchy Problem for the Equation \( \frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\varDelta u \) with Complex σ . J Math Sci 206, 171–180 (2015). https://doi.org/10.1007/s10958-015-2301-0
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DOI: https://doi.org/10.1007/s10958-015-2301-0