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The Non-Archimedean Stochastic Heat Equation Driven by Gaussian Noise

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Abstract

We introduce and study a new class of non-Archimedean stochastic pseudodifferential equations. These equations are the non-Archimedean counterparts of the classical stochastic heat equations. We show the existence and uniqueness of mild random field solutions for these equations.

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Acknowledgments

The author wishes to thank to Anatoly Kochubei and Sergii Torba for fruitful discussions and remarks. The author was partially supported by Conacyt (Mexico), Grant # 127794.

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  1. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Departamento de Matemáticas, Unidad Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, 76230, Santiago de Querétaro, Qro., Mexico

    W. A. Zúñiga-Galindo

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  1. W. A. Zúñiga-Galindo
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Correspondence to W. A. Zúñiga-Galindo.

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Communicated by Hans G. Feichtinger.

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Zúñiga-Galindo, W.A. The Non-Archimedean Stochastic Heat Equation Driven by Gaussian Noise. J Fourier Anal Appl 21, 600–627 (2015). https://doi.org/10.1007/s00041-014-9383-9

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  • DOI: https://doi.org/10.1007/s00041-014-9383-9

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