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pro vyhledávání: '"Kataria K"'
Autor:
Kataria, K. K., Vishwakarma, P.
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 classical birth-death process introduced by Feller (1939). We obtain the clos
Externí odkaz:
http://arxiv.org/abs/2410.17344
Autor:
Vishwakarma, P., Kataria, K. K.
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 in all possible directions such that the probability of simultaneous tr
Externí odkaz:
http://arxiv.org/abs/2408.12379
Autor:
Kataria, K. K., Vishwakarma, P.
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 fractional partial differential equations. A time-changed representati
Externí odkaz:
http://arxiv.org/abs/2407.15619
Autor:
Kataria, K. K., Dhillon, M.
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 such as the stable subordinator, inverse stable subordinator, and their
Externí odkaz:
http://arxiv.org/abs/2407.06156
Autor:
Dhillon, M., Kataria, K. K.
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 the case of countably infinite. The merged process is observed to be
Externí odkaz:
http://arxiv.org/abs/2310.06638
Autor:
Vishwakarma, P., Kataria, K. K.
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 equations that governs its state probabilities. The distribution function o
Externí odkaz:
http://arxiv.org/abs/2309.04969
We introduce a non-homogeneous version of the generalized counting process (GCP), namely, the non-homogeneous generalized counting process (NGCP). We time-change the NGCP by an independent inverse stable subordinator to obtain its fractional version,
Externí odkaz:
http://arxiv.org/abs/2210.03981
Autor:
Khandakar, M., Kataria, K. K.
Publikováno v:
Fractal and Fractional 7(1) (2023) 15
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes are limitin
Externí odkaz:
http://arxiv.org/abs/2206.04377
Autor:
Kataria, K. K., Khandakar, M.
In this paper, we introduce a generalized birth process (GBP) which performs jumps of size $1,2,\dots,k$ whose rates depend on the state of the process at time $t\geq0$. We derive a non-exploding condition for it. The system of differential equations
Externí odkaz:
http://arxiv.org/abs/2110.01190
Autor:
Kataria, K. K., Khandakar, M.
Publikováno v:
Fractional Calculus and Applied Analysis 25(5) (2022) 1873-1907
In this paper, we study a Skellam type variant of the generalized counting process (GCP), namely, the generalized Skellam process. Some of its distributional properties such as the probability mass function, probability generating function, mean, var
Externí odkaz:
http://arxiv.org/abs/2107.08307