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Derivation of the Hopf-Cole solution to Burgers' equation by stochastic integrals


Author: S. I. Rosencrans
Journal: Proc. Amer. Math. Soc. 32 (1972), 147-149
MSC: Primary 35.65; Secondary 60.00
DOI: https://doi.org/10.1090/S0002-9939-1972-0289953-5
MathSciNet review: 0289953
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Abstract: In this paper the Hopf-Cole solution to Burgers' equation is derived by use of stochastic integrals. First the equation is written in Hamilton-Jacobi form, and then, following an idea of Freidlin, the solution is differentiated along a Brownian motion.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289953-5
Keywords: Burgers' equation, stochastic integral, Ito's lemma
Article copyright: © Copyright 1972 American Mathematical Society