Random processes with common cotransition probabilities

The paper is devoted to the investigation of equivalent Markov diffusion processes. Analogues of the fundamental facts of the discrete theory are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 169–181, 1990.