Filtering with Marked Point Process Observations via Poisson Chaos Expansion

Journal Article · Sat Jun 15 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9189-6· OSTI ID:22156272

Sun Wei, E-mail: [e-mail] ^[1]; Zeng Yong, E-mail: [e-mail] ^[2]; Zhang Shu, E-mail: [e-mail] ^[1]

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1. Concordia University, Department of Mathematics and Statistics (Canada)
2. University of Missouri at Kansas City, Department of Mathematics and Statistics (United States)

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.

• OSTI ID: 22156272
• Journal Information: Applied Mathematics and Optimization, Vol. 67, Issue 3; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
CALCULATION METHODS
CHAOS THEORY
MATHEMATICAL SOLUTIONS
POISSON EQUATION
STOCHASTIC PROCESSES