Stochastic processes on random domains (Q1089991)

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