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A generalized ornstein-uhlenbeck process
Communications in Statistics - Theory and Methods, 1984We construct a generalized Ornstein-Uhlenbeck velocity process as a Gaussian process with a prescribed continuous covariance on (Hσ Sobolev space). It is shown that this can be realized in and solves a martingale problem analogous to the work in [7]. In fact for σ = 0 this gives their result.
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Ornstein-Uhlenbeck Processes as Bernstein Processes
1993Bernstein diffusions belong to a new class of time symmetric (but not time homogeneous) stochastic processes associated with the quantum dynamics of nonrelativistic particles in potentials. It is shown in which sense Feynman’s formal path integral method can be interpreted in terms of those processes, specially for the subset of Gaussian Bernstein ...
A. B. Cruzeiro, J. C. Zambrini
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