A probability approach to the heat equation
Author:
J. L. Doob
Journal:
Trans. Amer. Math. Soc. 80 (1955), 216-280
MSC:
Primary 60.0X
DOI:
https://doi.org/10.1090/S0002-9947-1955-0079376-0
MathSciNet review:
0079376
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References | Similar Articles | Additional Information
- [1] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0058896
- [2] J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86–121. MR 64347, https://doi.org/10.1090/S0002-9947-1954-0064347-X
- [3] J. L. Doob, Martingales and one-dimensional diffusion, Trans. Amer. Math. Soc. 78 (1955), 168–208. MR 70885, https://doi.org/10.1090/S0002-9947-1955-0070885-7
- [4] Robert Fortet, Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dérivées partielles du type parabolique, J. Math. Pures Appl. (9) 22 (1943), 177–243 (French). MR 12392
- [5] Philip Hartman and Aurel Wintner, On the solutions of the equation of heat conduction, Amer. J. Math. 72 (1950), 367–395. MR 36412, https://doi.org/10.2307/2372040
- [6] I. Petrowsky, Zur ersten Randwertaufgabe der Wärmeleitungsgleichung, Compositio Math. 1 (1935), 383–419 (German). MR 1556900
- [7] D. V. Widder, Positive temperatures on an infinite rod, Trans. Amer. Math. Soc. 55 (1944), 85–95. MR 9795, https://doi.org/10.1090/S0002-9947-1944-0009795-2
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1955-0079376-0
Article copyright:
© Copyright 1955
American Mathematical Society