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Dal'nevostochnyi Matematicheskii Zhurnal, 2015, Volume 15, Number 2, Pages 156–165
(Mi dvmg306)
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This article is cited in 2 scientific papers (total in 2 papers)
Some remarks on integral parameters of Wiener process
A. A. Vladimirov Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
Abstract:
It is shown that if generalized function $\rho\in W_2^{-1}[0,1]$ is a multiplier
of trace-class from space $W_2^1[0,1]$ to space $W_2^{-1}[0,1]$ then the distribution
of stochastic variable $\int_0^1\rho\xi^2\,dt$ (where $\xi$ is a Wiener process)
is determined by the spectrum of the boundary problem
$$
-y''=\lambda\rho y,\qquad y(0)=y'(1)=0,
$$
as in the case when $\rho$ is a measure. An example of generalized function
$\rho\in W_2^{-1}[0,1]$ that is not a multiplier of trace-class from $W_2^1[0,1]$
to $W_2^{-1}[0,1]$ is also given.
Key words:
generalized function, multiplier, Wiener process, operator of trace-class.
Received: 10.04.2015
Citation:
A. A. Vladimirov, “Some remarks on integral parameters of Wiener process”, Dal'nevost. Mat. Zh., 15:2 (2015), 156–165
Linking options:
https://www.mathnet.ru/eng/dvmg306 https://www.mathnet.ru/eng/dvmg/v15/i2/p156
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Abstract page: | 357 | Full-text PDF : | 122 | References: | 50 |
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