We construct an analog of the probabilistic representation for the solution of the string wave equation. Bibliography: 6 titles.
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A. D. Ventsel’, Theory of Random Processes [in Russian], Moscow (1975).
Kai Lai Chung and Zhongxin Zhao, From Brownian Motion to Schrödinger’s Equation, Springer–Verlag, Berlin Heidelberg (1995).
M. Freidlin, Functional Integration and Partial Differential Equations, Princeton Univ. Press, Princeton, New Jersey (1985).
I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev, “Probabilistic approximation for solutions of the Cauchy problem for some evolution equations,” Zap. Nauchn. Semin, POMI, 396, 111–141 (2011).
I. M. Gelfand and G. E. Shilov, Generalized Functions and Actions Upon Them [in Russian], Moscow (1958).
A. V. Skorokhod, Random Processes With Independent Increments [in Russian], Moscow (1986).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 408, 2012, pp. 289–302.
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Smorodina, N.V., Faddeev, M.M. The Probabilistic Approach to Solution of the String Wave Equation. J Math Sci 199, 228–235 (2014). https://doi.org/10.1007/s10958-014-1850-y
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DOI: https://doi.org/10.1007/s10958-014-1850-y