Zonova, Ya. S.

On $L_2$-small deviations of Slepian process

60G15 Gaussian processes

small deviations, Gaussian processes, exact asymptotics, matrix Sturm-Liouville problem

    The exact $L_2$-small deviation asymptotics is studied for the Slepian process $S(t) = W(t+a) - W(t)$, $t\in[0,1]$, where $W(t)$ is Brownian motion, for the parameter value $a= 1/3$. The result is based on Karhunen–Loève expansion which reduces the original problem to the study of a matrix Sturm-Liouville problem. Asymptotics is derived using Wenbo Li’s comparison theorem together with complex analysis methods.

Russian, 7 pp.

yana_kazinets@mail.ru

28.10.2026