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

Riccardo Gatto ()
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Riccardo Gatto: University of Bern

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 3, 843-864

Abstract: Abstract 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.

Keywords: Binomial; Negative binomial and poisson processes; Circular distribution; Defective density; Resultant length; Saddlepoint approximation; 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.), 62H11 Directional data; spatial statistics (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-016-9523-6

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