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

Gassiat P, Gess B, Lions P-L, Souganidis PE (2020)
PROBABILITY THEORY AND RELATED FIELDS 176(1-2): 421-448.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Gassiat, Paul; Gess, BenjaminUniBi; Lions, Pierre-Louis; Souganidis, Panagiotis E.
Abstract / Bemerkung
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.
Stichworte
Stochastic viscosity solutions; Stochastic Hamilton-Jacobi equations; Speed of propagation
Erscheinungsjahr
2020
Zeitschriftentitel
PROBABILITY THEORY AND RELATED FIELDS
Band
176
Ausgabe
1-2
Seite(n)
421-448
ISSN
0178-8051
eISSN
1432-2064
Page URI
https://pub.uni-bielefeld.de/record/2942092

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Gassiat P, Gess B, Lions P-L, Souganidis PE. Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. PROBABILITY THEORY AND RELATED FIELDS. 2020;176(1-2):421-448.
Gassiat, P., Gess, B., Lions, P. - L., & Souganidis, P. E. (2020). Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. PROBABILITY THEORY AND RELATED FIELDS, 176(1-2), 421-448. doi:10.1007/s00440-019-00921-5
Gassiat, P., Gess, B., Lions, P. - L., and Souganidis, P. E. (2020). Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. PROBABILITY THEORY AND RELATED FIELDS 176, 421-448.
Gassiat, P., et al., 2020. Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. PROBABILITY THEORY AND RELATED FIELDS, 176(1-2), p 421-448.
P. Gassiat, et al., “Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians”, PROBABILITY THEORY AND RELATED FIELDS, vol. 176, 2020, pp. 421-448.
Gassiat, P., Gess, B., Lions, P.-L., Souganidis, P.E.: Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. PROBABILITY THEORY AND RELATED FIELDS. 176, 421-448 (2020).
Gassiat, Paul, Gess, Benjamin, Lions, Pierre-Louis, and Souganidis, Panagiotis E. “Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians”. PROBABILITY THEORY AND RELATED FIELDS 176.1-2 (2020): 421-448.