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On a family of random operators
I. A. Ibragimovab, N. V. Smorodinaab, M. M. Faddeevb a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
Abstract:
Random operators arising in the construction of probabilistic representation
of the resolvent of the operator
$-\frac{1}{2}\,\frac{d}{dx}\bigl(b^2(x)\frac{d}{dx}\bigr)$ are considered and
shown to be integral with probability $1$. Properties of their kernels are
investigated.
Keywords:
random processes, local time, random operator.
Received: 05.02.2022 Revised: 11.02.2023
Citation:
I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a family of random operators”, Teor. Veroyatnost. i Primenen., 68:3 (2023), 544–564; Theory Probab. Appl., 68:3 (2023), 440–456
Linking options:
https://www.mathnet.ru/eng/tvp5555https://doi.org/10.4213/tvp5555 https://www.mathnet.ru/eng/tvp/v68/i3/p544
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Abstract page: | 163 | Full-text PDF : | 18 | References: | 36 | First page: | 18 |
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