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Theory of Probability and Mathematical Statistics

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Approximation of solution of the cable equation driven by a stochastic measure


Authors: B. I. Manikin and V. M. Radchenko
Journal: Theor. Probability and Math. Statist. 104 (2021), 103-112
MSC (2020): Primary 60H15, 60G57, 60H05
DOI: https://doi.org/10.1090/tpms/1148
Published electronically: September 24, 2021
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Abstract: The cable equation driven by a general stochastic measure is studied. We prove that convergence of the sequence of stochastic integrators implies the convergence of the sequence of solutions. Fourier series approximation of integrator is also considered.


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References
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Additional Information

B. I. Manikin
Affiliation: Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
Email: bmanikin@gmail.com

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
Email: vradchenko@univ.kiev.ua

Keywords: Stochastic measure, stochastic cable equation, mild solution
Received by editor(s): December 28, 2020
Published electronically: September 24, 2021
Article copyright: © Copyright 2021 Taras Shevchenko National University of Kyiv