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A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

  • A. JENTZEN (a1) and P. E. KLOEDEN (a2)
Abstract
Abstract

An existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise.

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Copyright
Corresponding author
For correspondence; e-mail: kloeden@math.uni-frankfurt.de
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This work has been supported by the DFG project ‘Pathwise numerics and dynamics of stochastic evolution equations’.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] A. Chojnowska-Michalik and B. Goldys , ‘Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces’, Probab. Theory Related Fields 102 (1995), 331356.

[2] G. Da Prato , A. Debussche and B. Goldys , ‘Some properties of invariant measures of non symmetric dissipative stochastic systems’, Probab. Theory Related Fields 123 (2002), 355380.

[7] R. Manthey and T. Zausinger , ‘Stochastic evolution equations in L2νρ’, Stoch. Stoch. Rep. 66 (1999), 3785.

[8] T. Müller-Gronbach and K. Ritter , ‘Lower bounds and nonuniform time discretization for approximation of stochastic heat equations’, Found. Comput. Math. 7 (2007), 135181.

[10] G. R. Sell and Y. You , Dynamics of Evolutionary Equations (Springer, New York, 2002).

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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