First-passage time, maximum displacement, and Kac’s solution of the telegrapher equation

Foong, See Kit

doi:10.1103/physreva.46.r707

Cited by 69 publications

(51 citation statements)

References 13 publications

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“…The classical case (c 1 c 2 c;I 12 1) has been studied in many papers and important probabilistic distributions and representations have been obtained independently by various authors and by different methods (for example, Orsingher [8], Foong [2], Foong and Kanno [3], Kabanov [4]). …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations

Beghin

Nieddu

Orsingher

2000

International Journal of Stochastic Analysis

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Section: Introductionmentioning

confidence: 99%

“…In this paper we consider the two-valued integrated telegraph signal with rightward velocity c 1 and leftward velocity -c 2 (cl,c2 > 0) and rates 11,12 of the occurrence of velocity switches, (1 when the current velocity is (-1) i+ lci, 1,2).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations

Beghin

Nieddu

Orsingher

2000

International Journal of Stochastic Analysis

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“…The process {V(t); t > 0} has been introduced by Goldstein [6] and extensively studied by many authors, including Kac [8] and Foong [4].…”

Section: A(t) = A(o)(--i) N(t) T > Omentioning

confidence: 99%

Limiting distributions of randomly accelerated motions

Conti¹,

Orsingher²

1997

Lith Math J

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In this paper, the process {X(t); t > 0}, representing the position of a uniformly accelerated particle (with Poisson-paced) changes of its acceleration, is studied. It is shown that the distribution of X (t) (suitably normalized), conditionally on the number n of changes of acceleration, tends in distribution to a normal variate as n goes to infinity. The asymptotic normality of the unconditional distribution of X(t) for large values of t is also shown. The study of these limiting distributions is motivated by the difficulty of evaluating exactly the conditional and unconditional probability laws of X(t). In fact, the results obtained in this paper permit us to give useful approximations of the probability distributions of the position of the particle.

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“…The relationships between the Goldstein-Kac model and physical processes, including some emerging effects of relativity theory, were examined in [1], [4], and [5]. Formulae for the distributions of the first exit time from a given interval and of the maximum displacement of the telegraph process were obtained in [8], [18], [19], and [20,Section 0.5]. The behavior of the telegraph The Euclidean distance between two telegraph processes 1173 process with absorbing and reflecting barriers was examined in [9] and [22].…”

Section: Introductionmentioning

confidence: 99%

Probability Distribution Function for the Euclidean Distance Between Two Telegraph Processes

Kolesnik

2014

Adv. Appl. Probab.

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Consider two independent Goldstein-Kac telegraph processes X 1 (t) and X 2 (t) on the real line R. The processes X k (t), k = 1, 2, describe stochastic motions at finite constant velocities c 1 > 0 and c 2 > 0 that start at the initial time instant t = 0 from the origin of R and are controlled by two independent homogeneous Poisson processes of rates λ 1 > 0 and λ 2 > 0, respectively. We obtain a closed-form expression for the probability distribution function of the Euclidean distance ρ(t) = |X 1 (t) − X 2 (t)|, t > 0, between these processes at an arbitrary time instant t > 0. Some numerical results are also presented.

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First-passage time, maximum displacement, and Kac’s solution of the telegrapher equation

Cited by 69 publications

References 13 publications

Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations

Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations

Limiting distributions of randomly accelerated motions

Probability Distribution Function for the Euclidean Distance Between Two Telegraph Processes

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