Some remarks on integral parameters of Wiener process

A. A. Vladimirov

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arXiv · 1212.1152

Some remarks on integral parameters of Wiener process

A. A. Vladimirov

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Abstract

We consider integrals $τ_ρ=\int_0^1ρξ^2\,dx$, where $ξ$ is Wiener process and $ρ$ is generalized function from some class of multipliers. In the case when multiplier $ρ$ belongs to the trace-class, it is shown that $τ_ρ$ has $χ^2$-distribution (or analogous). An example of multiplier $ρ$ not belonging to the trace-class is constructed.

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BibTeX RIS

A. A. Vladimirov. 2012-12-05. Some remarks on integral parameters of Wiener process. https://arxiv.org/abs/1212.1152

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