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Markovian extensions of a stochastic process

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  • Petrovic, Ljiljana

Abstract

The problem on existence of a minimal Markovian (in the wide sense) process which contains a given stochastic process as a component is considered and partially solved in Rozanov [1977. On Markovian extensions of random process. Theory Probab. Appl. 22 (1), 194-199]. In this paper the problem (to be formulated precisely below) of finding all Markovian (in the wide sense) extensions for a given stochastic process is solved. In the first part of this paper we give some definitions and known results related to splitting subspaces with respect to arbitrary Hilbert spaces. In the second part we apply these results to the problem of finding all Markovian (in the wide sense) extensions of an arbitrary stochastic process. The approach adopted in this paper is that of Lindquist and Picci [1985. On the stochastic realization problem. SIAM J. Control Optim. 17 (3), 365-389] and Rozanov [1977. On Markovian extensions of random process. Theory Probab. Appl. 22 (1), 194-199].

Suggested Citation

  • Petrovic, Ljiljana, 2008. "Markovian extensions of a stochastic process," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 810-814, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:810-814
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