Abstract
We introduce ``Markovian" cocycle perturbations of the group of unitary operators associated with a stochastic process with stationary increments, which are characterized by a localization of the perturbation to the algebra of past events. The definition we give is necessary because the Markovian perturbation of the group associated with a stochastic process with noncorrelated increments results in the perturbed group for which there exists a stochastic process with noncorrelated increments associated with it. On the other hand, some ``deterministic" stochastic process lying in the past can also be associated with the perturbed group. The model of Markovian perturbations describing all Markovian cocycles up to a unitary equivalence of the perturbations has been constructed. Using this model, we construct Markovian cocycles transforming Gaussian measures to the equivalent Gaussian measures.
Published Version
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