On the Relation of Zakai’s and Mortensen’s Equations

DOI10.1137/0321029zbMath0518.93062OpenAlexW2040128955MaRDI QIDQ3669282

Ioannis Karatzas, Václav E. Beneš

Publication date: 1983

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0321029

zbMATH Keywords

Zakai equation of nonlinear filteringpartially observed diffusionsMortensen's equation

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Dynamic programming in optimal control and differential games (49L20) Dynamic programming (90C39) Optimal stochastic control (93E20) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence of optimal solutions to problems involving randomness (49J55)

Related Items (12)

Maximum likelihood estimate for discontinuous parameter in stochastic hyperbolic systems ⋮ Mean Field Game Theory with a Partially Observed Major Agent ⋮ The probabilistic structure of controlled diffusion processes ⋮ New explicit filters and smoothers for diffusions with nonlinear drift and measurements ⋮ Operational absolutely optimal dynamic control of the stochastic differential plant's state by its output ⋮ Optimal finite-dimensional controller of the stochastic differential object's state by its output. I: Incomplete precise measurements ⋮ Operational-optimal finite-dimensional dynamic controller of the stochastic differential plant's state according to its output. I: General nonlinear case ⋮ Stochastic Control with Delayed Information and Related Nonlinear Master Equation ⋮ Application of conditional-optimal filter for synthesis of suboptimal control in the problem of optimizing the output of a nonlinear differential stochastic system ⋮ Filtering of diffusions controlled through their conditional measures^† ⋮ Adaptive boundary concentration control using Zakai equation ⋮ Mean Field Games with Partial Observation

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