Z. Brzezniak, Department of Mathematics, The University of Hull, Hull HU6 7RX, United Kingdom, e-mail: z.brzezniak@maths.hull.ac.uk; S. Peszat, Institute of Mathematics, Polish Academy of Sciences, Sw. Tomasza 30/7, 31-027 Krakow, Poland and Departement de Mathematiques, Universite Paris 13, Avenue J-B Clement, 93430 Villetaneuse, France, e-mail: napeszat@cyf-kr.edu.pl; J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-950 Warszawa, Poland and Mathematics Institute, Warwick University, Coventry, CV4 7AL, England, e-mail: zabczyk@impan.gov.pl
Abstract: Let $B$ be a Brownian motion, and let $\Cal C_ p$ be the space of all continuous periodic functions $f \Bbb R\to\Bbb R$ with period 1. It is shown that the set of all $f\in\Cal C_ p$ such that the stochastic convolution $X_{f,B}(t)= \int_0^tf(t-s)\dd B(s)$, $t\in[0,1]$ does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.
Keywords: stochastic convolutions, continuity of Gaussian processes, Gaussian trigonometric series
Classification (MSC 2000): 60H05, 60G15, 60G17, 60G50
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