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Forward and Backward Equations for an Adjoint Process

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Stochastic Processes

Abstract

A Markov chain is observed only through a noisy continuous observation process. A related optimal control problem is formulated in separated form by considering the related Zakai equation. An adjoint process is defined and shown to satisfy a forward stochastic partial differential equation, and also a system of backward parabolic equations.

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References

  1. A. Bensoussan, Lectures on stochastic control. In Lecture Notes in Mathematics, Vol. 972. Springer-Verlag, Berlin, Heidelberg, New York, 1982.

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Authors
  1. Robert J. Elliott
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  2. Hailiang Yang
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of North Carolina, Chapel Hill, NC, 27599-3260, USA

    Stamatis Cambanis  & Pranab K. Sen  & 

  2. Indian Statistical Institute, 203, B.T. Road, 700035, Calcutta, India

    Jayanta K. Ghosh

  3. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi, 110016, India

    Rajeeva L. Karandikar

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© 1993 Springer-Verlag New York, Inc.

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Elliott, R.J., Yang, H. (1993). Forward and Backward Equations for an Adjoint Process. In: Cambanis, S., Ghosh, J.K., Karandikar, R.L., Sen, P.K. (eds) Stochastic Processes. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7909-0_8

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  • DOI: https://doi.org/10.1007/978-1-4615-7909-0_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4615-7911-3

  • Online ISBN: 978-1-4615-7909-0

  • eBook Packages: Springer Book Archive

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