Geodesic
On the approximation of the solutions of some evolution equations by the expectations of functionals of random walks
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 242-252 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider some problems associated with a probabilistic representation and a probabilistic approximation of the Cauchy problem solution for the family of equations $\frac{\partial u}{\partial t}=\frac{\sigma^2}2\Delta u$ with a complex parameter $\sigma$ such that $\operatorname{Re}\sigma^2\geqslant0$. This equation coincides with the heat equation when $\operatorname{Im}\sigma=0$ and with the Schrödinger equation when $\operatorname{Re}\sigma^2=0$. 
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     title = {On the approximation of the solutions of some evolution equations by the expectations of functionals of random walks},
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S. V. Tsykin. On the approximation of the solutions of some evolution equations by the expectations of functionals of random walks. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 242-252. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a14/

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