Results 21 to 30 of about 4,870 (273)
On the integral of fractional Poisson processes [PDF]
Statistics & Probability Letters, 2013 In this paper we consider the Riemann--Liouville fractional integral $\mathcal{N}^{α,ν}(t)= \frac{1}{Γ(α)} \int_0^t (t-s)^{α-1}N^ν(s) \, \mathrm ds $, where $N^ν(t)$, $t \ge 0$, is a fractional Poisson process of order $ν\in (0,1]$, and $α> 0$. We give the explicit bivariate distribution $\Pr \{N^ν(s)=k, N^ν(t)=r \}$, for $t \ge s$, $r \ge k$, the ...
ORSINGHER, Enzo, POLITO, FEDERICO
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Fractional Generalizations of the Compound Poisson Process
, 2023 Abstract This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encom- passes existing variations as special cases. We derive its distributional properties, generalized fractional differential equations, and martingale ...
Gupta, Neha, Maheshwari, Aditya
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Large deviations for fractional Poisson processes [PDF]
Statistics & Probability Letters, 2013 We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance model with constant premium rate, i.i.d. light tail claim sizes, and a fractional Poisson claim number process.
BEGHIN, Luisa, Claudio Macci
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Fractional Discrete Processes: Compound and Mixed Poisson Representations [PDF]
Journal of Applied Probability, 2014 We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the ...
BEGHIN, Luisa, Claudio Macci
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Optimal Layer Reinsurance for Compound Fractional Poisson Model
Discrete Dynamics in Nature and Society, 2019 In this paper, we study the optimal retentions for an insurer with a compound fractional Poisson surplus and a layer reinsurance treaty. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are ...
Jiesong Zhang
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A fractional counting process and its connection with the Poisson process [PDF]
Latin American Journal of Probability and Mathematical Statistics, 2016 17 pages, 2 ...
DI CRESCENZO, Antonio +2 more
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Laplace-Laplace analysis of the fractional Poisson process [PDF]
, 2012 We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.
R. Gorenflo, MAINARDI, FRANCESCO
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A generalization of the space-fractional Poisson process and its connection to some Lévy processes [PDF]
Electronic Communications in Probability, 2016 This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It turns out that this generalization can be put in relation to a specific subordination of a homogeneous Poisson ...
Federico Polito, Enrico Scalas
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Convoluted Fractional Poisson Process
Latin American Journal of Probability and Mathematical Statistics, 2021 In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking the discrete convolution with respect to space variable in the system of fractional differential equations that governs its state probabilities. We call the introduced process as the convoluted fractional Poisson process (CFPP).
Kumar Kataria, Kuldeep +1 more
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Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes [PDF]
Journal of Statistical Physics, 2012 In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_α(t)$, $N_β(t)$, $t>0$, we show that $N_α(N_β(t)) \overset{\text{d}}{=} \sum_{j=1}^{N_β(t)} X_j$, where the $X_j$s are Poisson random variables. We present a series of similar cases, the most general
ORSINGHER, Enzo, POLITO, FEDERICO
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