On the Asymmetric Telegraph Processes

López, Oscar; Ratanov, Nikita

doi:10.1239/jap/1402578644

Cited by 30 publications

(28 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Restricting the attention to some recent contributions, we also mention Beghin et al [3] and López and Ratanov [26] for the asymmetric telegraph process, Bogachev and Ratanov [5] for the distribution of the occupation time of the positive half-line for the telegraph process, Crimaldi et al [7] for a telegraph process driven by certain random trials, De Gregorio and Macci [8] for the large deviation principle applied to the telegraph process, Di Crescenzo and Martinucci [10] for a damped telegraph process, Fontbona et al [16] for the long-time behavior of an ergodic variant of the telegraph process, Stadje and Zacks [39] for the telegraph process with random velocities, Pogorui et al [30] for estimates of the number of level-crossings for the telegraph process, Di Crescenzo and Zacks [11] for the analysis of a generalized telegraph process perturbed by Brownian motion, De Gregorio and Orsingher [9] and Garra and Orsingher [18] for certain multidimensional extension of the telegraph process. Moreover, D'Ovidio et al [14] investigate other types of multidimensional extensions of the telegraph process, whose distribution is related to space-time fractional n-dimensional telegraph equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Telegraph Process with Elastic Boundary at the Origin

Crescenzo

Martinucci

Zacks

2017

Methodol Comput Appl Probab

View full text Add to dashboard Cite

We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability α, or reflected upwards, with probability 1 − α. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Figure 2: Density f A 0 (y), given in(26), for (λ, µ) = (2, 0.5) (left-hand side) and (λ, µ) = (2, 1.5) (right-hand side) with α = 0.1, 0.3, 0.5, 0.7, 0.9 from bottom to top near the origin.…”

mentioning

confidence: 99%

Telegraph Process with Elastic Boundary at the Origin

Crescenzo

Martinucci

Zacks

2017

Methodol Comput Appl Probab

View full text Add to dashboard Cite

show abstract

“…Masoliver and Weiss computed mean first passage times for a telegrapher's equation with spatially-dependent switching rates [31], which may allow us to incorporate biologically realistic geometries where switching rates depend on vesicle position. Additional studies examine the telegrapher's equation with asymmetric rates λ [26], non-equal velocities [27,46], and different waitingtime distributions [59], which would make it possible to incorporate kinesin and dynein motors, which are known to have distinct properties from myosin [34]. Spatially-dependent velocities have also been considered for tau-covered microtubules [37], which may be relevant in diseased or pathologically-formed spines.…”

Section: Discussionmentioning

confidence: 99%

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

Park,

Singh,

Fai

2021

Preprint

View full text Add to dashboard Cite

We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of the mean first passage time for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.

show abstract

“…The well-known formulae for the (conditional) distribution of T(t) follow from (A.1): [14] or see in the book by Kolesnik and Ratanov,[12,(4.1.15)].…”

Section: Appendix: the Telegraph Processmentioning

confidence: 99%

Ornstein-Uhlenbeck Processes of Bounded Variation

Ratanov

2020

Methodol Comput Appl Probab

Self Cite

View full text Add to dashboard Cite

Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval I such that the process starting from the internal point of I always remains within I. Starting outside, this process a. s. reaches this interval in a finite time. The distribution of the time for which the process falls into this interval is obtained explicitly. The certain formulae for the mean and the variance of this process are obtained on the basis of the joint distribution of the telegraph process and its integrated copy. Under Kac's rescaling, the limit process is identified as the classical Ornstein-Uhlenbeck process.

show abstract

On the Asymmetric Telegraph Processes

Cited by 30 publications

References 22 publications

Telegraph Process with Elastic Boundary at the Origin

Telegraph Process with Elastic Boundary at the Origin

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

Ornstein-Uhlenbeck Processes of Bounded Variation

Contact Info

Product

Resources

About