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Zbl 0621.60040
Dynkin, E.B.; Fitzsimmons, P.J.
Stochastic processes on random domains. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 23, Suppl., 379-396 (1987). ISSN 0246-0203

This paper is devoted to study stochastic processes with a random parameter set. The main result is a characterization of the finite dimensional distributions of a stochastic process whose parameter domain is a random open convex subset of $R\sp d$. This result generalizes a previous work of {\it S. E. Kuznetsov} [Teor. Veroyatn. Primen. 18, 596- 601 (1973; Zbl 0296.60049)], and its proof is based on two theorems: \par (1) A characterization of the finite-dimensional distributions of a random open convex subset of $R\sp d$, which is a refinement of a theorem of {\it G. Choquet} [Ann. Inst. Fourier 5, 131-295 (1955; Zbl 0064.351)]. \par (2) A general "inverse limit" theorem that extends a result of {\it K. Y. Hu}. Some applications to the construction of Markov processes with regular paths are also discussed.
[D.Nualart]

MSC 2000:: *60G05 Foundations of stochastic processes
60D05 Geometric probability
60G60 Random fields
60J45 Probabilistic potential theory

Keywords: projective systems of measures; stochastic processes with a random parameter set; random open convex subset; construction of Markov processes with regular paths

Citations: Zbl 0296.60049; Zbl 0064.351

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