Paper Info
Title
Saddlepoint approximation to the distribution of the total distance of the von Mises-Fisher continuous time random walk.
Abstract
This article considers the random walk over Rp, with any p ≥ 2, where a particle starts at the origin and progresses stepwise with fixed step lengths and von Mises–Fisher distributed step directions. The total number of steps follows a continuous time counting process. The saddlepoint approximation to the distribution of the distance between the origin and the position of the particle at any time is derived. Despite the p-dimensionality of the random walk, the computation of the proposed saddlepoint approximation is one-dimensional and thus simple. The high accuracy of the saddlepoint approximation is illustrated by a numerical comparison with Monte Carlo simulation.
Year
DOI
Venue
2018
10.1016/j.amc.2017.12.030
Applied Mathematics and Computation
Keywords
Field
DocType
Bessel function,Directional distribution,Legendre–Fenchel transform,Poisson process
Applied mathematics,Monte Carlo method,Counting process,Mathematical analysis,Random walk,Continuous-time random walk,von Mises yield criterion,Poisson process,Mathematics,Bessel function,Computation
Journal
Volume
ISSN
Citations 
324
0096-3003
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Riccardo Gatto1125.65