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Linear transformations of Gaussian processes

M. Erraoui, Y. Ouknine

Abstract


We consider certain classes of linear transformations of Gaussian processes. In particular we characterize those transformations which preserve the law of the original process. Furthermore we give the explicit Karhunen-Lo`eve expansion for particular transformed processes.
Therefore we calculate the Laplace transform of some functionals of these processes.

Keywords


Brownian motion, Karhunen-Lo`eve expansion, Gaussian processes, Quadratic functionals.

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