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

Gatto, Riccardo (2018). Saddlepoint approximation to the distribution of the total distance of the von Mises-Fisher continuous time random walk. Applied mathematics and computation, 324, pp. 285-294. Elsevier 10.1016/j.amc.2017.12.030

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Gatto, Riccardo

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0096-3003

Publisher:

Elsevier

Language:

English

Submitter:

Riccardo Gatto

Date Deposited:

20 May 2019 12:17

Last Modified:

01 Jun 2020 02:30

Publisher DOI:

10.1016/j.amc.2017.12.030

BORIS DOI:

10.7892/boris.126286

URI:

https://boris.unibe.ch/id/eprint/126286

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