Some remarks on integral parameters of Wiener process

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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