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Heat equation in a multidimensional domain with a general stochastic measure


Authors: I. M. Bodnarchuk and G. M. Shevchenko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 1-17
MSC (2010): Primary 60H15; Secondary 60G17, 60G57
DOI: https://doi.org/10.1090/tpms/991
Published electronically: February 7, 2017
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Abstract: Stochastic heat equation on $ [0,T]\times \mathbb{R}^d$, $ d\ge 1$, driven by a general stochastic measure $ \mu (t)$, $ t\in [0,T]$, is studied in this paper. The existence, uniqueness, and Hölder regularity of a mild solution are proved.


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Additional Information

I. M. Bodnarchuk
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: robeiko_i@ukr.net

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/991
Keywords: Stochastic measure, stochastic heat equation, mild solution, H\"older condition, Besov space
Received by editor(s): July 28, 2015
Published electronically: February 7, 2017
Additional Notes: The paper was prepared following the talk at the International 5conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
The results of the paper have also been presented at the conference “Stochastic Processes in Abstract Spaces (SPAS 2015)”, October 14–16, 2015
Article copyright: © Copyright 2017 American Mathematical Society