Approximations for the likelihood ratio for continuous multi-parameter stochastic processes

Rob Luesink, Arunabha Bagchi

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    35 Downloads (Pure)

    Abstract

    Based on finitely additive white noise theory, one may derive the likelihood ratio for random variables with values in any Hilbert space. This includes stochastic processes, defined on a one- or multi-dimensional continuous-parameter bounded domain. In certain circumstances, the likelihood ratio for continuous processes may be computed directly. In general however, one will have to approximate the likelihood ratio. In this paper approximations for the likelihood ratios for continuous-parameter processes are studied. Starting from a sequence of finite dimensional projection operators in the Hilbert space, strongly converging to identity, the authors show that the likelihood ratios for the projected processes converge to the likelihood ratio for the original process. Discretization of the stochastic process turns out to be one of the possibilities for such approximations. The discretization method is expected to give good results for signals satisfying elliptic PDEs, because discretization of these processes leads to nearest neighbor models, for which the likelihood ratio has been obtained in Luesink (1992).
    Original languageEnglish
    Title of host publicationProceedings of the 32nd IEEE Conference on Decision and Control
    Subtitle of host publicationDecember 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA
    Place of PublicationPiscataway, NJ, USA
    PublisherIEEE
    Pages1559-1563
    Number of pages5
    ISBN (Print)9780780312982
    DOIs
    Publication statusPublished - 13 Jan 1993
    Event32nd IEEE Conference on Decision and Control, CDC 1993 - San Antonio, United States
    Duration: 15 Dec 199317 Dec 1993
    Conference number: 32

    Publication series

    NameProceedings IEEE Conference on Decision and Control (CDC
    PublisherIEEE
    ISSN (Print)0191-2216

    Conference

    Conference32nd IEEE Conference on Decision and Control, CDC 1993
    Abbreviated titleCDC
    CountryUnited States
    CitySan Antonio
    Period15/12/9317/12/93

    Fingerprint

    Likelihood Ratio
    Stochastic Processes
    Approximation
    Hilbert space
    Discretization
    Elliptic PDE
    Discretization Method
    Projection Operator
    Process Parameters
    White noise
    Bounded Domain
    Nearest Neighbor
    Random variable
    Converge

    Cite this

    Luesink, R., & Bagchi, A. (1993). Approximations for the likelihood ratio for continuous multi-parameter stochastic processes. In Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA (pp. 1559-1563). (Proceedings IEEE Conference on Decision and Control (CDC). Piscataway, NJ, USA: IEEE. https://doi.org/10.1109/CDC.1993.325449
    Luesink, Rob ; Bagchi, Arunabha. / Approximations for the likelihood ratio for continuous multi-parameter stochastic processes. Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Piscataway, NJ, USA : IEEE, 1993. pp. 1559-1563 (Proceedings IEEE Conference on Decision and Control (CDC).
    @inproceedings{bbcb98e37a22443a8241c8883c22ab60,
    title = "Approximations for the likelihood ratio for continuous multi-parameter stochastic processes",
    abstract = "Based on finitely additive white noise theory, one may derive the likelihood ratio for random variables with values in any Hilbert space. This includes stochastic processes, defined on a one- or multi-dimensional continuous-parameter bounded domain. In certain circumstances, the likelihood ratio for continuous processes may be computed directly. In general however, one will have to approximate the likelihood ratio. In this paper approximations for the likelihood ratios for continuous-parameter processes are studied. Starting from a sequence of finite dimensional projection operators in the Hilbert space, strongly converging to identity, the authors show that the likelihood ratios for the projected processes converge to the likelihood ratio for the original process. Discretization of the stochastic process turns out to be one of the possibilities for such approximations. The discretization method is expected to give good results for signals satisfying elliptic PDEs, because discretization of these processes leads to nearest neighbor models, for which the likelihood ratio has been obtained in Luesink (1992).",
    author = "Rob Luesink and Arunabha Bagchi",
    year = "1993",
    month = "1",
    day = "13",
    doi = "10.1109/CDC.1993.325449",
    language = "English",
    isbn = "9780780312982",
    series = "Proceedings IEEE Conference on Decision and Control (CDC",
    publisher = "IEEE",
    pages = "1559--1563",
    booktitle = "Proceedings of the 32nd IEEE Conference on Decision and Control",
    address = "United States",

    }

    Luesink, R & Bagchi, A 1993, Approximations for the likelihood ratio for continuous multi-parameter stochastic processes. in Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Proceedings IEEE Conference on Decision and Control (CDC, IEEE, Piscataway, NJ, USA, pp. 1559-1563, 32nd IEEE Conference on Decision and Control, CDC 1993, San Antonio, United States, 15/12/93. https://doi.org/10.1109/CDC.1993.325449

    Approximations for the likelihood ratio for continuous multi-parameter stochastic processes. / Luesink, Rob; Bagchi, Arunabha.

    Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Piscataway, NJ, USA : IEEE, 1993. p. 1559-1563 (Proceedings IEEE Conference on Decision and Control (CDC).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - Approximations for the likelihood ratio for continuous multi-parameter stochastic processes

    AU - Luesink, Rob

    AU - Bagchi, Arunabha

    PY - 1993/1/13

    Y1 - 1993/1/13

    N2 - Based on finitely additive white noise theory, one may derive the likelihood ratio for random variables with values in any Hilbert space. This includes stochastic processes, defined on a one- or multi-dimensional continuous-parameter bounded domain. In certain circumstances, the likelihood ratio for continuous processes may be computed directly. In general however, one will have to approximate the likelihood ratio. In this paper approximations for the likelihood ratios for continuous-parameter processes are studied. Starting from a sequence of finite dimensional projection operators in the Hilbert space, strongly converging to identity, the authors show that the likelihood ratios for the projected processes converge to the likelihood ratio for the original process. Discretization of the stochastic process turns out to be one of the possibilities for such approximations. The discretization method is expected to give good results for signals satisfying elliptic PDEs, because discretization of these processes leads to nearest neighbor models, for which the likelihood ratio has been obtained in Luesink (1992).

    AB - Based on finitely additive white noise theory, one may derive the likelihood ratio for random variables with values in any Hilbert space. This includes stochastic processes, defined on a one- or multi-dimensional continuous-parameter bounded domain. In certain circumstances, the likelihood ratio for continuous processes may be computed directly. In general however, one will have to approximate the likelihood ratio. In this paper approximations for the likelihood ratios for continuous-parameter processes are studied. Starting from a sequence of finite dimensional projection operators in the Hilbert space, strongly converging to identity, the authors show that the likelihood ratios for the projected processes converge to the likelihood ratio for the original process. Discretization of the stochastic process turns out to be one of the possibilities for such approximations. The discretization method is expected to give good results for signals satisfying elliptic PDEs, because discretization of these processes leads to nearest neighbor models, for which the likelihood ratio has been obtained in Luesink (1992).

    U2 - 10.1109/CDC.1993.325449

    DO - 10.1109/CDC.1993.325449

    M3 - Conference contribution

    SN - 9780780312982

    T3 - Proceedings IEEE Conference on Decision and Control (CDC

    SP - 1559

    EP - 1563

    BT - Proceedings of the 32nd IEEE Conference on Decision and Control

    PB - IEEE

    CY - Piscataway, NJ, USA

    ER -

    Luesink R, Bagchi A. Approximations for the likelihood ratio for continuous multi-parameter stochastic processes. In Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Piscataway, NJ, USA: IEEE. 1993. p. 1559-1563. (Proceedings IEEE Conference on Decision and Control (CDC). https://doi.org/10.1109/CDC.1993.325449