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A Probabilistic Approximation of the Evolution Operator exp (t (S∇, ∇)) with a Complex Matrix S

We consider some problems concerning a probabilistic interpretation of the Cauchy problem solution for the equation \( \frac{\partial u}{\partial t}=\frac{1}{2}\left(S\nabla, \kern0.33em \nabla \right)u, \) where S is a symmetric complex matrix such that Re S ≥ 0.

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Correspondence to I. A. Ibragimov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 134–144.

Translated by S. Yu. Pilyugin.

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Ibragimov, I.A., Smorodina, N.V. & Faddeev, M.M. A Probabilistic Approximation of the Evolution Operator exp (t (S∇, ∇)) with a Complex Matrix S. J Math Sci 244, 789–795 (2020). https://doi.org/10.1007/s10958-020-04652-0

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