7 papers · 2 filters
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…