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Forward and Backward Equations for an Adjoint Process

In: Stochastic Processes

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  • Robert J. Elliott
  • Hailiang Yang

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.

Suggested Citation

  • Robert J. Elliott & Hailiang Yang, 1993. "Forward and Backward Equations for an Adjoint Process," Springer Books, in: Stamatis Cambanis & Jayanta K. Ghosh & Rajeeva L. Karandikar & Pranab K. Sen (ed.), Stochastic Processes, pages 61-69, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-7909-0_8
    DOI: 10.1007/978-1-4615-7909-0_8
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