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

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  • Gatto, R.

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.

Suggested Citation

  • Gatto, R., 2018. "Saddlepoint approximation to the distribution of the total distance of the von Mises–Fisher continuous time random walk," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 285-294.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:285-294
    DOI: 10.1016/j.amc.2017.12.030
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    References listed on IDEAS

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    1. Riccardo Gatto, 2017. "Saddlepoint approximation to the distribution of the total distance of the continuous time random walk," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(12), pages 1-13, December.
    2. Riccardo Gatto, 2017. "Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 843-864, September.
    3. Ryszard Kutner & Jaume Masoliver, 2017. "The continuous time random walk, still trendy: fifty-year history, state of art and outlook," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(3), pages 1-13, March.
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