Limit theorem for maximum of the storage process with fractional Brownian motion as input

Jürg Hüsler and Vladimir Piterbarg ()

Stochastic Processes and their Applications, 2004, vol. 114, issue 2, 231-250

Abstract: The maximum MT of the storage process Y(t)=sups[greater-or-equal, slanted]t(X(s)-X(t)-c(s-t)) in the interval [0,T] is dealt with, in particular, for growing interval length T. Here X(s) is a fractional Brownian motion with Hurst parameter, 0 u for u-->[infinity]. Using this expression the convergence P MT G(x) as T-->[infinity] is derived where uT(x)-->[infinity] is a suitable normalization and G(x)=exp(-exp(-x)) the Gumbel distribution. Also the relation to the maximum of the process on a dense grid is analysed.

Keywords: Storage; process; Maximum; Limit; distribution; Fractional; Brownian; motion; Dense; grid (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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