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

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arxiv 2305.17276 v2 pith:O5B4ZCYU submitted 2023-05-26 math.PR math.AP

Yuri Bakhtin , Douglas Dow This is my paper · ORCID
classification math.PRmath.AP
keywords differentiabilitydynamiceffectiveenvironmentsequationslagrangianproblemsrandom
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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.

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  1. Classification of the limit shape for 1+1-dimensional FPP

    math.PR 2024-11 conditional novelty 7.0 of 10

    In a planar FPP model with deterministic vertical weights, the limit shape has a flat vertical edge if and only if the horizontal edge weight distribution charges its infimum.

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