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Planar piecewise linear random motions with jumps
Author(s) -
Garra Roberto,
Orsingher Enzo,
Ratanov Nikita
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4552
Subject(s) - mathematics , jump , piecewise linear function , poisson distribution , gaussian , piecewise , planar , mathematical analysis , exponential function , exponential distribution , statistical physics , statistics , physics , computer graphics (images) , quantum mechanics , computer science
In this paper, we study persistent piecewise linear multidimensional random motions. Their velocities, switching at Poisson times, are uniformly distributed on a sphere. The changes of direction are accompanied with subsequent jumps of random length and of uniformly distributed orientation. In this paper, we obtain some useful properties and formulae of distributions of these processes. In particular, we get these distributions in the cases of jumps with Gaussian and exponential distributions of jump magnitudes.