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Feynman formulas for second-order parabolic equations with variable coefficients. (English) Zbl 1285.81030
Summary: Feynman formulas giving a representation of the solution of a Cauchy problem for a second-order parabolic differential equation are obtained.

MSC:
 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry 35K20 Initial-boundary value problems for second-order parabolic equations
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References:
 [1] Gadella, M; Smolyanov, O G, Feynman formulas for particles with position-dependent mass, Dokl. Akad. Nauk, 418, 727-730, (2008) · Zbl 1159.35426 [2] Smolyanov, O G; Tokarev, A G; Truman, A, Hamiltonian Feynman path integrals via the Chernoff formula, J. of Math. Phys., 43, 5161-5171, (2002) · Zbl 1060.58009 [3] Smolyanov, O G; Weizsäcker, H; Wittich, O, Brownian motion on a manifold as limit of stepwise conditioned standard Brownian motions, Can. Math. Soc. Conf. Proc., 29, 589-602, (2000) · Zbl 0978.58015 [4] Obrezkov, O O; Smolyanov, O G; Truman, A, The generalized Chernoff theorem and randomized Feynman formula, Dokl. Akad. Nauk, 400, 596-601, (2005)
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