Random motion with gamma-distributed alternating velocities in biological modeling
Antonio Di Crescenzo,Barbara Martinucci +1 more
- pp 163-170
TLDR
A generalized integrated telegraph process is analyzed, where the random times between consecutive velocity reversals are gamma-distributed, and the probability law and the mean are obtained.Abstract:
Motivated by applications in mathematical biology concerning randomly alternatingmotion ofmicro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are gamma-distributed, and perform an alternating renewal process. We obtain the probability law and the mean of the process.read more
Citations
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Journal ArticleDOI
A damped telegraph random process with logistic stationary distribution
TL;DR: In this article, a stochastic process that describes a finite-velocity damped motion on the real line is introduced, where the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters.
Journal ArticleDOI
Persistent random walk of cells involving anomalous effects and random death.
TL;DR: A stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction, and it is shown that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process.
Journal ArticleDOI
A generalized telegraph process with velocity driven by random trials
TL;DR: In this paper, the authors considered a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions, and investigated the probability law of the process and the mean of the velocity of the moving particle.
Journal ArticleDOI
A generalized telegraph process with velocity driven by random trials
TL;DR: In this paper, the authors considered a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions, and investigated the probability law of the process and the mean of the velocity of the moving particle.
Journal ArticleDOI
Some Results on the Telegraph Process Confined by Two Non-Standard Boundaries
TL;DR: In this article, the authors analyzed the one-dimensional telegraph random process confined by two boundaries, 0 and H > 0, and provided various results on the expected values of the renewal cycles and of the absorption time.
References
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Models of dispersal in biological systems
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Journal ArticleDOI
Some applications of persistent random walks and the telegrapher's equation
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Journal ArticleDOI
A biased random walk model for the trajectories of swimming micro-organisms.
Nicholas A. Hill,D.-P. Häder +1 more
TL;DR: The motion of swimming micro-organisms that have a preferred direction of travel, such as single-celled algae moving upwards (gravitaxis) or towards a light source (phototaxis), is modelled as the continuous limit of a correlated and biased random walk as the time step tends to zero.