Robust Filtering Algorithm for Markov Jump Processes with High-Frequency Counting Observations

2020 ◽  
Vol 81 (4) ◽  
pp. 575-588
Author(s):  
A. V. Borisov
Keyword(s):  
High Frequency ◽  
Jump Processes ◽  
Robust Filtering ◽  
Markov Jump ◽  
Filtering Algorithm ◽  
Markov Jump Processes ◽  
Frequency Counting

scholarly journals Heat Release by Controlled Continuous-Time Markov Jump Processes

2013 ◽  
Vol 150 (1) ◽  
pp. 181-203 ◽  
Author(s):  
Paolo Muratore-Ginanneschi ◽  
Carlos Mejía-Monasterio ◽  
Luca Peliti
Keyword(s):  
Heat Release ◽  
Continuous Time ◽  
Jump Processes ◽  
Markov Jump ◽  
Markov Jump Processes

scholarly journals Optimal Filtering of Markov Jump Processes Given Observations with State-Dependent Noises: Exact Solution and Stable Numerical Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 506
Author(s):  
Andrey Borisov ◽  
Igor Sokolov
Keyword(s):  
Exact Solution ◽  
Nonlinear Filtering ◽  
Innovation Process ◽  
Jump Processes ◽  
State Transitions ◽  
Observation System ◽  
Optimal Filtering ◽  
Markov Jump ◽  
Approximation Accuracy ◽  
Markov Jump Processes

The paper is devoted to the optimal state filtering of the finite-state Markov jump processes, given indirect continuous-time observations corrupted by Wiener noise. The crucial feature is that the observation noise intensity is a function of the estimated state, which breaks forthright filtering approaches based on the passage to the innovation process and Girsanov’s measure change. We propose an equivalent observation transform, which allows usage of the classical nonlinear filtering framework. We obtain the optimal estimate as a solution to the discrete–continuous stochastic differential system with both continuous and counting processes on the right-hand side. For effective computer realization, we present a new class of numerical algorithms based on the exact solution to the optimal filtering given the time-discretized observation. The proposed estimate approximations are stable, i.e., have non-negative components and satisfy the normalization condition. We prove the assertions characterizing the approximation accuracy depending on the observation system parameters, time discretization step, the maximal number of allowed state transitions, and the applied scheme of numerical integration.

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