Saddlepoint approximation to the distribution of the total distance of the von Mises–Fisher continuous time random walk

R. Gatto

Applied Mathematics and Computation, 2018, vol. 324, issue C, 285-294

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.

Keywords: Bessel function; Directional distribution; Legendre–Fenchel transform; Poisson process (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:324:y:2018:i:c:p:285-294

DOI: 10.1016/j.amc.2017.12.030

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