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Averaging principle for the heat equation driven by a general stochastic measure

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  • Radchenko, Vadym

Abstract

We study the one-dimensional stochastic heat equation in the mild form driven by a general stochastic measure μ, for μ we assume only σ-additivity in probability. The time averaging of the equation is considered, uniform a. s. convergence to the solution of the averaged equation is obtained.

Suggested Citation

  • Radchenko, Vadym, 2019. "Averaging principle for the heat equation driven by a general stochastic measure," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 224-230.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:224-230
    DOI: 10.1016/j.spl.2018.11.024
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    References listed on IDEAS

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    1. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    2. Fu, Hongbo & Wan, Li & Liu, Jicheng & Liu, Xianming, 2018. "Weak order in averaging principle for stochastic wave equation with a fast oscillation," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2557-2580.
    3. Vadym Radchenko, 2014. "Stochastic Partial Differential Equations Driven by General Stochastic Measures," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 143-156, Springer.
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