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On Berman Functions

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Let Z(t)=exp2BH(t)-t2H,t∈R with BH(t),t∈R a standard fractional Brownian motion (fBm) with Hurst parameter H∈(0,1] and define for x non-negative the Berman function BZ(x)=EI{ϵ0(RZ)>x}ϵ0(RZ)∈(0,∞),where the random varia... ...