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    On strong causal binomial approximation for stochastic processes

    199526_199526.pdf (122.8Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, N. 2014. On strong causal binomial approximation for stochastic processes. Discrete and Continuous Dynamical Systems Series B. 19 (6): pp. 1549-1562.
    Source Title
    Discrete and Continuous Dynamical Systems Series B
    DOI
    10.3934/dcdsb.2014.19.1549
    ISSN
    1531-3492
    Remarks

    This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems Series B following peer review. The definitive publisher-authenticated version Dokuchaev, N. 2014. On strong causal binomial approximation for stochastic processes. Discrete and Continuous Dynamical Systems Series B. 19 (6): pp. 1549-1562 is available online at: http://doi.org/10.3934/dcdsb.2014.19.1549

    URI
    http://hdl.handle.net/20.500.11937/27706
    Collection
    • Curtin Research Publications
    Abstract

    This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process. In addition, possibility of approximation of solutions of stochastic differential equations by solutions of ordinary equations with binary noise is established. Some consequences for the financial modelling and options pricing models are discussed.

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