Abstract
We consider, in a Hilbert space U, a class of Gaussian processes defined by a linear filter with a cylindrical Wiener process as input process. This noise is used as an additive perturbation to a family of fractional order (in time) partial differential equations. We give conditions such that the stochastic convolution process is well defined, both in finite time horizon and in an infinite interval. An important example of noise that is contained in the paper is the fractional Brownian motion.
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Bonaccorsi, S. (2007). Volterra Equations Perturbed by a Gaussian Noise. In: Dalang, R.C., Russo, F., Dozzi, M. (eds) Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8458-6_4
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DOI: https://doi.org/10.1007/978-3-7643-8458-6_4
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