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On the Markov property of a stochastic difference equation

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  • Ferrante, Marco
  • Nualart, David

Abstract

In the present paper we study the one-dimensional stochastic difference equation Xn+1 = Xn + f(Xn) + [sigma](Xn)[xi]n, n [epsilon] {0, ..., N - 1}, N \s#62; 6, with linear boundary conditions at the endpoints. We present an existence and uniqueness result and study the Markov property of the solution. We are able to prove that the solution is a reciprocal Markov chain if and only if the functions f(x) and [sigma](x) are both polynomial out of a "small" interval, whose length depends on f and the boundary condition.

Suggested Citation

  • Ferrante, Marco & Nualart, David, 1994. "On the Markov property of a stochastic difference equation," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 239-250, August.
  • Handle: RePEc:eee:spapps:v:52:y:1994:i:2:p:239-250
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    Cited by:

    1. Dalang, Robert C. & Hou, Qiang, 1997. "On Markov properties of Lévy waves in two dimensions," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 265-287, December.
    2. Baccin, Maria C. & Ferrante, Marco, 1995. "On a stochastic delay difference equation with boundary conditions and its Markov property," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 131-146, November.

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