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Seminar on Stochastic Analysis, Random Fields and Applications V pp 37–55Cite as

Volterra Equations Perturbed by a Gaussian Noise

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Part of the book series: Progress in Probability ((PRPR,volume 59))

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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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38050, Povo (Trento), Italia

    Stefano Bonaccorsi

Authors
  1. Stefano Bonaccorsi
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Editor information

Editors and Affiliations

  1. Institut de Mathématiques, Ecole Polytechnique Fédérale, CH-1005, Lausanne, Switzerland

    Robert C. Dalang

  2. Département de Mathématiques, Institut Galilée, Université Paris 13, F-95430, Villetaneuse, France

    Francesco Russo

  3. Institut Elie Cartan, Université Henri Poincaré, B.P. 239, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    Marco Dozzi

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© 2007 Birkhäuser Verlag Basel/Switzerland

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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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