Geodesic
An analogue of the Feynman–Kac formula for a high-order operator
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 81-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we construct a probabilistic approximation of the evolution operator $\exp\bigl(t\bigl({\frac{(-1)^{m+1}}{(2m)!}\,\frac{d^{2m}}{dx^{2m}}+V}\bigr)\bigr)$ in the form of expectations of functionals of a point random field. This approximation can be considered as a generalization of the Feynman–Kac formula to the case of a differential equation of order $2m$.
Mots-clés : evolution equations, Feynman–Kac formula.
Keywords: Poisson random measures 
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M. V. Platonova. An analogue of the Feynman–Kac formula for a high-order operator. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 81-99. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a4/

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