arXiv subjects

Rohini Bhagwanrao Pote

Publications and source records attributed to Rohini Bhagwanrao Pote.

3 recordsLinked to original sources

arXiv2026

On a Telegraph Process with Generalized Mittag-Leffler Waiting times and Velocity Driven by Random trials

We study a generalized telegraph process in which the velocity is governed by random trials by considering the specific distribution of waiting times. In this telegraph process, a particle moving on real line may change its direction whenever there is an arrival in a counting process. This direction change is driven by the outcomes of random trials. In the first case, random trials are independent and identically distributed, and waiting times have Mittag-Leffler distribution. In the second case, random trials follow Pólya urn scheme and the first waiting time is generalized Mittag-Leffler distributed whereas other waiting times have Mittag-Leffler distribution. In both cases, we obtain the discrete component of their probability law. Also, absolutely continuous components of their conditional probability law given initial velocity are derived. The plots of absolutely continuous components of their probability law are compared for different parameters. Conditional on the initial velocity, the distributions of $n$th event time of counting processes associated with these telegraph processes are obtained.

math.PR↗

arXiv2026

On Time-Changed Birth-Death Processes with Catastrophes

We study two time-changed variants of the birth-death process with catastrophe where the time-changing components are the first hitting times of the stable subordinator and the tempered stable subordinator. For both the processes, we derive the governing system of fractional differential equations for their state probabilities. The Laplace transforms of these state probabilities are obtained in terms of those of the corresponding time-changed birth-death processes without catastrophes. We obtain the distribution of catastrophe occurrence times as well as the sojourn times within non-zero states. We study distributional properties of the first visit time to state zero in a particular case. Also, the first occurrence time of an effective catastrophe is studied. Moreover, we study the time-changed linear birth-death processes with catastrophes, derive the explicit expressions for its state probabilities, expectation and variance. For a specific case, we compare the expectation plots across different parameter values and provide an algorithm for simulating sample paths with illustrative plots.

math.PR↗

arXiv2025

On Mixed Time-Changed Erlang Queue

We study a time-changed variant of the Erlang queue by taking the first hitting time of a mixed stable subordinator as the time-changing component. We call it the mixed time-changed Erlang queue. We derive the system of fractional differential equations that governs its state probabilities. The explicit expressions for the state probabilities of mixed time-changed Erlang queue and their Laplace transform are derived. Equivalently, it is represented in terms of phases and its mean queue length is obtained. Also, some distributional properties of the mixed time-changed Erlang queue such as the distribution of its inter-arrival times, inter-phase times, service times and busy period are derived. Later, its conditional waiting time is discussed and two plots of sample paths simulation are presented.

math.PR↗