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

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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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     author = {M. V. Platonova},
     title = {An analogue of the {Feynman--Kac} formula for a~high-order operator},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {81--99},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a4/}
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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/