Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions

Gatto, Riccardo (2017). Large Deviations Approximations to Distributions of the Total Distance of Compound Random Walks with von Mises Directions. Methodology and Computing in Applied Probability, 19(3), pp. 843-864. Springer 10.1007/s11009-016-9523-6

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This article considers the planar random walk where the direction taken by each consecutive step follows the von Mises distribution and where the number of steps of the random walk is determined by the class of inhomogeneous birth processes. Saddlepoint approximations to the distribution of the total distance covered by the random walk, i.e. of the length of the resultant vector of the individual steps, are proposed. Specific formulae are derived for the inhomogeneous Poisson process and for processes with linear contagion, which are the binomial and the negative binomial processes. A numerical example confirms the high accuracy of the proposed saddlepoint approximations.

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