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• W2045603699 abstract "Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity 1, 6, 8, 10 or a random diffusivity. 5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new." @default.
• W2045603699 created "2016-06-24" @default.
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• W2045603699 date "1969-02-01" @default.
• W2045603699 modified "2023-10-12" @default.
• W2045603699 title "RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS" @default.
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• W2045603699 doi "https://doi.org/10.1073/pnas.62.2.305" @default.
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