Some remarks on integral parameters of Wiener process

2012/12/05 by A. A. Vladimirov, Vladimirov, A. A.
Mathematics · #34L20 #47B10 #60G15 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:34L20 #msc:47B10 #msc:60G15

paper · pdf · doi:10.48550/arxiv.1212.1152

8 pages

arxiv created 2012/12/05 · arxiv updated 2012/12/06

Abstract

We consider integrals τ_ρ=∫₀¹ρξ² 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 χ²-distribution (or analogous). An example of multiplier ρ not belonging to the trace-class is constructed.

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