Keywords
- Heat Equation
- Integral Kernel
- Schrodinger Equation
- Probabilistic Interpretation
- Bernstein Transition
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References
R.P. Feynman, Rev. Mod. Phys., 20, 267 (1948); with A.R. Hibbs, "Quantum Mechanics and Path Integrals", McGraw-Hill N.Y. (1965).
E. Nelson, J. Math. Phys. 5, 332(1964); S. Albeverio and R. Hoegh-Krohn, "Mathematical Theory of Feynman Path Integrals", Lect. Notes in Math. 523, Springer-Verlag, Berlin (1976); D. Elworthy and A. Truman, Ann. Inst. Henri Poincaré Vol. 41, no 2, 115 (1984).
M. Kac, "On some connections between probability theory and differential and integral equations" in Proc. of 2st Berkeley Symposium on Probability and Statistics, J. Neyman Ed., Univ. of California Press, Berkeley (1951).
N. Wienner, J. Math. Phys. 2, 132 (1923).
I. Fenyes, Zeitsch. für Phys., 132, 81 (1952) E. Nelson, Phys. Rev. 150, 1079 (1966); "Quantum Fluctuations", Princeton Univ. Press (1985).
E. Schrödinger, Ann. Inst. Henri Poincaré 11, 300 (1932).
S. Bernstein, "Sur les liaisons entre les grandeurs aléatoires", Verh des intern. Mathematikerkongr., Zurich, Band 1 (1932); R. Fortet, J. Math. Pures et Appl. IX, 83 (1940); A. Beurling, Annals of Math., 72, 1, 189 (1960); B. Jamison, Z. Wahrscheinlich, ver Gebiete 30, 65 (1964).
J.C. Zambrini, J. Math. Phys. 27, 9, 2307 (1986); "Euclidean Quantum Mechanics, Phys. Rev. A, 35, 9 3631 (1987); with S. Albeverio and K. Yasue "Hilbert space approach to Euclidean quantum mechanics", to appear.
J.L. Doob, A Markov chain Theorem. Probability and Statistic, in The Harold Cramér Volume, N.Y. Wiley (1959).
K. Yasue, J. Math. Phys. 22, 1010 (1981); J. Funct. Anal. 41, 327 (1981).
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© 1988 Springer-Verlag
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Zambrini, J.C. (1988). New probabilistic approach to the classical heat equation. In: Truman, A., Davies, I.M. (eds) Stochastic Mechanics and Stochastic Processes. Lecture Notes in Mathematics, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077929
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DOI: https://doi.org/10.1007/BFb0077929
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