Brownian motion with a parabolic drift and airy functions
نویسندگان
چکیده
منابع مشابه
The maximum of Brownian motion with parabolic drift ( Extended abstract )
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. This has some applications in algorithmic and data structures analysis. We give series expansions and integral formulas for the distribution and the first two moments, together with n...
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We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.
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dXt = dWt + dAt , where Wt is d-dimensional Brownian motion with d ≥ 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure πi as ∫ t 0 f (Xs)ds does to the measure f (x)dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures πi are members of the Kato class Kd−1. As a typical example,...
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Let (Bδ(t))t≥0 be a Brownian motion starting at 0 with drift δ > 0. Define by induction S1 = − inf t≥0 Bδ(t), ρ1 the last time such that Bδ(ρ1) = −S1, S2 = sup 0≤t≤ρ1 Bδ(t), ρ2 the last time such that Bδ(ρ2) = S2 and so on. Setting Ak = Sk + Sk+1 ; k ≥ 1, we compute the law of (A1, · · · , Ak) and the distribution of ((Bδ(t + ρl) − Bδ(ρl) ; 0 ≤ t ≤ ρl−1 − ρl))2≤l≤k for any k ≥ 2, conditionally ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 1989
ISSN: 0178-8051,1432-2064
DOI: 10.1007/bf00343738