Indranil Chowdhury, Espen R. Jakobsen, Miłosz Krupski
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引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6302-6336, October 2024. Abstract. We introduce a class of fully nonlinear mean field games posed in [math]. We justify that they are related to controlled local or nonlocal diffusions, and more generally in our setting, to a new control interpretation involving time change rates of stochastic (Lévy) processes. The main results are the existence and uniqueness of solutions under general assumptions. These results are applied to nondegenerate equations—including both local second-order and nonlocal with fractional Laplacians. Uniqueness holds under the monotonicity of couplings and convexity of the Hamiltonian, but neither monotonicity nor convexity need to be strict. We consider a rich class of nonlocal operators and processes and develop tools to work in the whole space without explicit moment assumptions.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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