A Bayes formula for Gaussian noise processes and its applications

Pranab K. Mandal, V. Mandrekar

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)
    34 Downloads (Pure)

    Abstract

    An elementary approach is used to derive a Bayes-type formula, extending the Kallianpur--Striebel formula for the nonlinear filters associated with the Gaussian noise processes. In the particular cases of certain Gaussian processes, recent results of Kunita and of Le Breton on fractional Brownian motion are derived. We also use the classical approximation of the Brownian motion by the Ornstein--Uhlenbeck dispersion process to solve the "instrumentability" problem of Balakrishnan. We give precise conditions
    Original languageEnglish
    Pages (from-to)852-871
    Number of pages15
    JournalSIAM journal on control and optimization
    Volume39
    Issue number3
    DOIs
    Publication statusPublished - 2000

    Keywords

    • Filtering
    • Gaussian noise process
    • Ornstein-Uhlenbeck dispersion process
    • Zakai equation
    • Bayes formula
    • fractional Brownian motion

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