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Stochastic Integral with respect to Cylindrical Wiener Process

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arxiv math/0511512 v1 pith:WHW22Y5K submitted 2005-11-21 math.PR math.FA

classification math.PRmath.FA
keywords integralconstructioncylindricalintroducedprocessrespectstochasticwiener
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This paper is devoted to a construction of the stochastic It\^o integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conditional Speed and Shape Corrections for Travelling Wave Solutions to Stochastically Perturbed Reaction-Diffusion Systems

    math.AP 2025-02 accept novelty 7.0 of 10

    The authors rigorously justify small-noise expansions for stochastic traveling waves, showing wave-speed corrections can be computed to arbitrary order with quantified errors.

  2. Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves

    nlin.PS 2025-11 conditional novelty 6.0 of 10

    Noise slows spiral-wave rotation at second order in noise strength, via an always-negative instantaneous term plus an orbital-drift term that can have either sign.

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