21 citations · 123 across the 38 of their papers we have counts for
42 papers
Amnesic Elephant Random Walk with Polynomially Decaying Step Sizes
Shyan Ghosh, Manisha Dhillon, Kuldeep Kumar Kataria
In this paper, we introduce an amnesic elephant random walk with polynomially decaying step sizes. The walk retains the loss of memory effect of amnesic ERW, however its step sizes…
On a Telegraph Process with Generalized Mittag-Leffler Waiting times and Velocity Driven by Random trials
Rohini Bhagwanrao Pote, Kuldeep Kumar Kataria
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…
On Elephant Random Walk with Delayed Amnesia
Manisha Dhillon, Shyan Ghosh, Kuldeep Kumar Kataria
In this paper, we introduce a modified elephant random walk that exhibits a transition from a uniform memory mechanism to a selective amnesic memory mechanism. Using a vector marti…
On Time-Changed Birth-Death Processes with Catastrophes
Kuldeep Kumar Kataria, Rohini Bhagwanrao Pote
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 tem…
On multidimensional elephant random walk with stops and random step sizes
Shyan Ghosh, Manisha Dhillon, Kuldeep Kumar Kataria
In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several convergence results for the number of moves, including the l…
Multivariate Generalized Counting Process via Gamma Subordination
Manisha Dhillon, Kuldeep Kumar Kataria, Shyan Ghosh
In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial pro…
Fractional Compound Poisson Random Fields on Plane
P. Vishwakarma, K. K. Kataria
We study a compound Poisson random field on plane and examine its various fractional variants. We derive the distributions of these random fields and in some particular cases, obta…
On Mixed Time-Changed Erlang Queue
Rohini Bhagwanrao Pote, Kuldeep Kumar Kataria
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-change…
Tempered Erlang Queue with Multiple Arrivals
Manisha Dhillon, Kuldeep Kumar Kataria
In this paper, we introduce and study a time-changed variant of the Erlang queue with multiple arrivals where the time-changing component used is the first hitting time of a temper…
On Two Parameter Time-Changed Poisson Random Fields with Drifts
Pradeep Vishwakarma, Manisha Dhillon, Kuldeep Kumar Kataria
We study the composition of bivariate Lévy process with bivariate inverse subordinator. The explicit expressions for its dispersion and auto correlation matrices are obtained. Also…
On Multiparameter Generalized Counting Process and its Time-Changed Variants
Manisha Dhillon, Kuldeep Kumar Kataria
We introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the mul…
On a Fractional Variant of Linear Birth-Death Process
Manisha Dhillon, Pradeep Vishwakarma, Kuldeep Kumar Kataria
We introduce and study a fractional variant of the linear birth-death process, namely, the generalized fractional linear birth-death process (GFLBDP) which is defined by taking the…
Generalized Counting Process with Random Drift and Different Brownian Clocks
Mostafizar Khandakar, Manisha Dhillon, Kuldeep Kumar Kataria
In this paper, we introduce drifted versions of the generalized counting process (GCP) with a deterministic drift and a random drift. The composition of stable subordinator with an…
On Elephant Random Walk with Random Memory
M. Dhillon, K. K. Kataria
In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant…
On Erlang Queue with Multiple Arrivals and its Time-changed Variant
R. B. Pote, K. K. Kataria
We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an…
Time-changed multiparameter Poisson processes and martingales
Pradeep Vishwakarma, Kuldeep Kumar Kataria
We consider a multiparameter extension of the homogeneous Poisson counting process, namely, the multiparameter Poisson process (MPP). We derive its various distributional propertie…
Iterated Generalized Counting Process and its Extensions
M. Dhillon, K. K. Kataria
In this paper, we study the composition of two independent GCPs which we call the iterated generalized counting process (IGCP). Its distributional properties such as the transition…
On Time-Changed Linear Birth-Death Process with Immigration at Extinction
K. K. Kataria, P. Vishwakarma
We study an immigration effect in the time-changed linear birth-death process where the immigration occurs only if the population goes extinct. We call this process as the time-fra…
On Transient Probabilities of Fractional Birth-Death Process
K. K. Kataria, P. Vishwakarma
We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classic…
Generalized Birth-Death Process on Finite Lattice
P. Vishwakarma, K. K. Kataria
We consider a generalized birth-death process (GBDP) whose state space is a finite subset of a -dimensional lattice. It is assumed that there can be a jump of finite step size i…
On the Multivariate Generalized Counting Process and its Time-Changed Variants
K. K. Kataria, M. Dhillon
In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes s…
Fractional Poisson Random Fields on
K. K. Kataria, P. Vishwakarma
In this paper, we consider a fractional Poisson random field (FPRF) on positive plane. It is defined as a process whose one dimensional distribution is the solution of a system of…
On the Superposition and Thinning of Generalized Counting Processes
M. Dhillon, K. K. Kataria
In this paper, we study the merging and splitting of generalized counting processes (GCPs). First, we study the merging of a finite number of independent GCPs and then extend it to…
On the Generalized Birth-Death Process and its Linear Versions
P. Vishwakarma, K. K. Kataria
In this paper, we consider a generalized birth-death process (GBDP) and examined its linear versions. Using its transition probabilities, we obtain the system of differential equat…