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Mean Square Continuity of Ornstein-Uhlenbeck Processes in Banach Spaces

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Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 55))

Abstract

We consider the following stochastic abstract Cauchy problem:dX (t) = AX (t) dt + B dW (t) t > 0where A is the generator of a Co—semigroup S = S(t)t>o on a separable real Banach spaceE Bis a bounded linear operator from a separable real Hilbert spaceHintoEand WH (t)t>ois a cylindrical Wiener process with Cameron-Martin spaceH.For the precise definition of this concept we refer to [3].

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References

  1. P. Billingsley, Convergence of probability measures. John Wiley and Sons, New YorkLondon-Sydney-Toronto, 1968.

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Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Hull, Hull, HU6 7RX, England

    Z. Brzeźniak

  2. School of Mathematics, The University of New South Wales, Sydney, 2052, Australia

    B. Goldys

  3. Department of Applied Mathematical Analysis, Technical University of Delft, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    J. M. A. M. van Neerven

Authors
  1. Z. Brzeźniak
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  2. B. Goldys
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  3. J. M. A. M. van Neerven
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Trento, via Sommarive 14, 38050, Povo, Trento, Italy

    Mimmo Iannelli

  2. Institute of Mathematics and Informatics, University of Mons-Hainaut, 20, place du Parc, 7000, Mons, Belgium

    Günter Lumer

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© 2003 Springer Basel AG

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Brzeźniak, Z., Goldys, B., van Neerven, J.M.A.M. (2003). Mean Square Continuity of Ornstein-Uhlenbeck Processes in Banach Spaces. In: Iannelli, M., Lumer, G. (eds) Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics. Progress in Nonlinear Differential Equations and Their Applications, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8085-5_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8085-5_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9433-3

  • Online ISBN: 978-3-0348-8085-5

  • eBook Packages: Springer Book Archive

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