On near optimal trajectories for a game associated with the ∞-Laplacian

A two-player stochastic differential game representation has recently been obtained for solutions of the equation −Δ ∞ u  =  h in a domain with Dirichlet boundary condition, where h is continuous and takes values in . Under appropriate assumptions, including smoothness of u , we identify a family of...

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Bibliographic Details
Published in:Probability theory and related fields 2011-12, Vol.151 (3-4), p.509-528
Main Authors: Atar, Rami, Budhiraja, Amarjit
Format: Article
Language:English
Subjects:
Boundary conditions
Differential equations
Differential games
Dirichlet problem
Economics
Exact sciences and technology
Finance
Game theory
Games
General topics
Insurance
Laplace transforms
Management
Markov processes
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability and statistics
Probability Theory and Stochastic Processes
Quantitative Finance
Saddle points
Sciences and techniques of general use
Smoothness
Statistics for Business
Stochastic models
Studies
Theoretical
Trajectory optimization
Viscosity
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Summary:A two-player stochastic differential game representation has recently been obtained for solutions of the equation −Δ ∞ u  =  h in a domain with Dirichlet boundary condition, where h is continuous and takes values in . Under appropriate assumptions, including smoothness of u , we identify a family of diffusion processes that may arise as the vanishing δ limit law of the state process, when both players play δ -optimally. We also identify the limit law of the state process under a sequence of near saddle points.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-010-0306-7