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Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems
self-similar long-range dependence Gaussian processes Brownian Motion
2009/3/27
In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance ∫0min(s,t) ua [(t-u)b+(s-u)b]du,parameters a > -1, -1 < b ≤ 1, |b| ≤ 1 + a, corresp...
Distribution of the Brownian motion on its way to hitting zero
Brownian motion probability density
2009/3/23
For the one-dimensional Brownian motion $B=(Bt)t≥ 0$, started at $x>0$, and the first hitting time $τ=inf{t≥ 0:Bt=0}$, we find the probability density of $Buτ$ for a $uin(0,1)$, i.e. of the Brownian ...
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
Hermite power variation fractional Brownian motion
2009/3/20
Let q≥2 be a positive integer, B be a fractional Brownian motion with Hurst index H∈(0,1), Z be an Hermite random variable of index q, and Hq denote the q-th Hermite polynomial. For any n≥1, set Vn=∑0...