Large deviations of infinite intersections of events in Gaussian processes

Michel Mandjes, Petteri Mannersalo, Ilkka Norros and Miranda van Uitert

Stochastic Processes and their Applications, 2006, vol. 116, issue 9, 1269-1293

Abstract: Consider events of the form {Zs>=[zeta](s),s[set membership, variant]S}, where Z is a continuous Gaussian process with stationary increments, [zeta] is a function that belongs to the reproducing kernel Hilbert space R of process Z, and is compact. The main problem considered in this paper is identifying the function [beta]*[set membership, variant]R satisfying [beta]*(s)>=[zeta](s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when [zeta](s)=s for s[set membership, variant][0,1] and Z is either a fractional Brownian motion or an integrated Ornstein-Uhlenbeck process.

Keywords: Sample-path; large; deviations; Dominating; point; Reproducing; kernel; Hilbert; space; Minimum; norm; problem; Fractional; Brownian; motion; Busy; period (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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