Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes

Abstract

A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.

11 pages, 3 figures

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Duality and hidden symmetries in interacting particle systems
• Extended duality relations between birth-death processes and partial differential equations
• Algebraic probability, classical stochastic processes, and counting statistics

Cited by in corpus (4)

• Duality in stochastic processes from the viewpoint of basis expansions
• Permutation of Tensor-Train Cores for Computing Moments on Stochastic Differential Equations
• Connection among stochastic Hamilton-Jacobi-Bellman equation, path-integral, and Koopman operator on nonlinear stochastic optimal control
• Duality-based calculations for transition probabilities in stochastic chemical reactions