P. Vishwakarma

Moments approach for the elephant random walk

Pradeep Vishwakarma

We discuss the method of moments for the one-dimensional elephant random walk (ERW). We first derive a differential recurrence relation for the characteristic function of the ERW,…

Convergence of random sums in non-commutative probability

Arup Bose, Pradeep Vishwakarma

Random sums of independent random variables have been extensively studied in classical probability theory. We consider random sums of self-adjoint variables from a non-commutative…

Revisiting Toeplitz and Hankel random matrices via $*$ -convergence of circulant-type matrices

Arup Bose, Pradeep Vishwakarma

We establish the joint $*$ -convergence of a random circulant matrix and a specific deterministic diagonal matrix. We also show that the empirical spectral distributions of skew-cir…

Some Spatial Point Processes of Poisson Family

Pradeep Vishwakarma

Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce…

Patterned matrices with random walk entries

Arup Bose, Pradeep Vishwakarma

It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matr…

Skellam Processes via Multiparameter Poisson Process

Pradeep Vishwakarma

We introduce a mltiparameter version of Skellam point process via multiparameter Poisson processes. Its distributional properties are studied in detail. Its compound representation…

Skellam Random Fields and Their Fractional Variants

Pradeep Vishwakarma

We study some Skellam-type spatial point processes. As a particular case, we consider a Skellam random field (SRF) on the positive quadrant of the plane, which is a two parameter L…

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 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 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…

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…

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 $q$ -dimensional lattice. It is assumed that there can be a jump of finite step size i…