Random Motions at Finite Speed in Higher Dimensions

Kolesnik, Alexander D.

doi:10.1007/s10955-008-9532-0

Cited by 40 publications

(61 citation statements)

References 11 publications

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“…Thus, we are extending some of the results found in [1,2,7]. Furthermore, we consider this random motion in one-, two-, three-, and four-dimensions, and we show that the transition densities in some of the cases have an explosive growth near the sphere of their singularity.…”

supporting

confidence: 72%

“…and constant speed or constant velocity, so their processes are Markovian, e.g., [1,2], and references therein. One-dimensional non-Markovian random evolutions generalizes these results by changing the underlying Poisson process, where motion is driven by an alternating semi-Markov process with Erlang distributed interrenewal times [3][4][5][6].…”

mentioning

confidence: 99%

“…A random walk with steps of Dirichlet distributed lengths and uniformly distributed changes of direction is reported in [9,10]. Closed-form expressions for the transition densities in the cases of two-and four-dimensional Markovian random motions have been derived by E. Orsingher and A. de Gregorio in [1], and by A. Kolesnik in [2].…”

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confidence: 99%

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Random Motion with Uniformly Distributed Directions and Random Velocity

Pogorui

Rodríguez‐Dagnino

2012

J Stat Phys

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In this paper we deal with uniformly distributed direction of motion or isotropic motion at random speed or velocity where the direction alternations occur according to the renewal epochs of a general distribution. We derive the renewal equation for the characteristic function of the transition density of the multidimensional motion. Then, by using the renewal equation, we study the behavior of the transition density near the sphere of its singularity for one-, two-, three-, and four-dimensional cases. To illustrate our solution methodology we present detailed calculations of many solvable examples.

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confidence: 99%

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Random Motion with Uniformly Distributed Directions and Random Velocity

Pogorui

Rodríguez‐Dagnino

2012

J Stat Phys

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“…In this work, we consider multidimensional random motions with uniformly distributed directions with K-Erlang distributed steps. Our analysis is based on random evolutions on a semi-Markov media, and we have extended many of the results of [12].…”

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confidence: 98%

“…The function ϕ η (ω) will be denoted as ϕ(ω) in the rest of the paper. We should notice that ϕ(ω) was also obtained in [12] by using a different method.…”

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confidence: 99%

Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations

Pogorui

Rodríguez‐Dagnino

2011

J Stat Phys

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We study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a K-Erlang pdf. At first sight, our generalizations of previous Markovian results appears to be a small step, however, it must be seen as an important non-Markovian case where we have found closed-form expressions for the pdf and the conditional characteristic function of this semi-Markov transport process. We present detailed calculations of a three-dimensional example for the 2-Erlang case, which is important not only from physical applications point of view but also to understand more general models. For instance, in principle the example of the 2-Erlang case can be extended to a K-Erlang case (K = 3, 4, . . .) but some of the mathematical expressions may be cumbersome.

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Stochastic Models of Transport Processes

Kolesnik¹

2011

International Encyclopedia of Statistical Science

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Random Motions at Finite Speed in Higher Dimensions

Cited by 40 publications

References 11 publications

Random Motion with Uniformly Distributed Directions and Random Velocity

Random Motion with Uniformly Distributed Directions and Random Velocity

Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations

Stochastic Models of Transport Processes

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