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Transformation of diffusion fields created by two Wiener processes. (English) Zbl 0830.60069
Consider the problem of existence and construction of the diffusion field \(\xi (z)\) determined by the system of Itô stochastic differential equations: \[ d_k \xi = f_k (z, \xi) dt_k + g_k(z, \xi) dw_k (t_k), \quad \xi (z_0) = \xi_0,\;k = 1,2. \] For the solution of the given problem we use the method of transformation of diffusion fields, which arises from the generalization of our method of diffusion processes transformation. The basic formulations of this paper have been previously reported without proofs [the author, Sov. Math., Dokl. 35, 56- 58 (1987); translation from Dokl. Akad. Nauk SSSR 292, 276-279 (1987; Zbl 0627.60052)]. Most of the notations adopted here are the same as in [H. Korezlioglu, P. Lefort and G. Mazziotto, in: Processus aléatoires à deux indices. Lect. Notes Math. 863, 245-274 (1981; Zbl 0456.60073)].
60J60 Diffusion processes
60J65 Brownian motion