Gaussian-Markov processes and a boundary value problem

/rlOy is also continuous if y E E. We shall also show our solution satisfies a backward version of (1.1)-(1.4), and is unique. The solution will involve an expectation over the sample functions of a Gaussian-Markov process. An n-dimensional version of a similar system has been studied by M. Rosenblatt [21] and D. Ray [20], for the Wiener process where B(t) =0. M. Kac studied the Wiener version in [15], as did R. H. Cameron in [5], subject to different boundary conditions. A backward time version of (1.1) with different boundary conditions was studied by the author in [3], as an underlying theorem for generalized Schroedinger equations. The need to develop forward time forms of such equations, and to weaken the hypotheses on the potential 0(y, t) helped motivate this paper. R. K. Getoor considered (1.1) for stationary Markov processes in [11], [12]. The principal reference is D. A. Darling and A. J. F. Siegert [8]. They proved that if:

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