Kolmogorov equations on spaces of measures associated to nonlinear filtering processes

DOI10.1016/j.spa.2023.04.013zbMath1517.60092arXiv2107.11865MaRDI QIDQ6157007

Mattia Martini

Publication date: 19 June 2023

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.11865

zbMATH Keywords

stochastic filteringmeasure-valued processesbackward Kolmogorov equationsdifferential equations on spaces of measures

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Signal detection and filtering (aspects of stochastic processes) (60G35) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items (2)

Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces ⋮ On smooth approximations in the Wasserstein space

Cites Work

• An infinite-dimensional approach to path-dependent Kolmogorov equations
• Fundamentals of stochastic filtering
• Unique characterization of conditional distributions in nonlinear filtering
• Backward SDEs for optimal control of partially observed path-dependent stochastic systems: A control randomization approach
• Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
• On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations
• On uniqueness of solutions for the stochastic differential equations of nonlinear filtering
• Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
• Mean-field stochastic differential equations and associated PDEs
• Long time average of first order mean field games and weak KAM theory
• Topics in Uniform Approximation of Continuous Functions
• Mean field approach to stochastic control with partial information
• Fokker–Planck–Kolmogorov Equations
• The Master Equation and the Convergence Problem in Mean Field Games
• Probabilistic Theory of Mean Field Games with Applications I
• Derivative formulas in measure on Riemannian manifolds
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