Differentiability of the effective Lagrangian for Hamilton–Jacobi–Bellman equations in dynamic random environments

Yuri Bakhtin; Douglas Dow

doi:10.1007/s40072-025-00371-2

Differentiability of the effective Lagrangian for Hamilton–Jacobi–Bellman equations in dynamic random environments

Yuri Bakhtin, Douglas Dow

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental solutions in the associated homogenization problems for HJB equations are classical.

Original language	English (US)
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
DOIs	https://doi.org/10.1007/s40072-025-00371-2
State	Accepted/In press - 2025

Keywords

Directed polymers
Effective Lagrangian
Geodesics
HJB equations
Homogenization
Random environment
Shape function
Shear invariance

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1007/s40072-025-00371-2

Cite this

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title = "Differentiability of the effective Lagrangian for Hamilton–Jacobi–Bellman equations in dynamic random environments",

abstract = "We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental solutions in the associated homogenization problems for HJB equations are classical.",

keywords = "Directed polymers, Effective Lagrangian, Geodesics, HJB equations, Homogenization, Random environment, Shape function, Shear invariance",

author = "Yuri Bakhtin and Douglas Dow",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

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doi = "10.1007/s40072-025-00371-2",

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AU - Bakhtin, Yuri

AU - Dow, Douglas

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025

Y1 - 2025

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KW - Effective Lagrangian

KW - Geodesics

KW - HJB equations

KW - Homogenization

KW - Random environment

KW - Shape function

KW - Shear invariance

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Differentiability of the effective Lagrangian for Hamilton–Jacobi–Bellman equations in dynamic random environments

Abstract

Keywords

ASJC Scopus subject areas

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