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.

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