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arXiv · 1805.08477

Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians

Paul Gassiat·Benjamin Gess·Pierre-Louis Lions·Panagiotis E. Souganidis
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Abstract

We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of dependence is bounded by a multiple of the length of the "skeleton" of the path, that is a piecewise linear path obtained by connecting the successive extrema of the original one. When the driving path is a Brownian motion, we prove that its skeleton has almost surely finite length. We also discuss the optimality of the estimate.

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Paul Gassiat, Benjamin Gess, Pierre-Louis Lions, Panagiotis E. Souganidis. 2018-05-22. Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. https://arxiv.org/abs/1805.08477

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