Wiener case Clause Samples

Wiener case where Ln(D, H, m) = exp − Dt−H/(n−H) − mt(1−H)/(n−H) ∫∞ . 1 . 2 Σ2Σ When X is a Wiener process (i. e., X = σB1/2), the density of τD is available in explicit form [15]: Additionally, the following asymptotic was derived for the large values of level D: 2πσt P(τD ∈ dt) = √ 3/2 exp (D mt)2 Σ . − − 2σ2t ▇▇ ▇▇m E [τn ] D −n = m Dn =:fτ (t|D) dt . (2) In this case, the corresponding expected value E[τD] is the ratio between the given amount of the work D and the mean processing rate [15]: for all n ≥ 1, m > 0, from which it is quite straightfor- ▇▇▇d to show that for all n ≥ 1, τD Ln 1 D −→ m as D → ∞ E [τ ] = D .