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Theorems on large deviations for the sum of random number of summands
Lietuvos Matematikos Rinkinys, 2010 In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i =
Aurelija Kasparavičiūtė +1 more
doaj +1 more source
Modern Stochastics: Theory and Applications, 2020 Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound ...
Nikolaos D. Macheras +1 more
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Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case [PDF]
, 2012 Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure.
Lambert, Amaury, Simatos, Florian
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Zanco Journal of Humanity Sciences, 2022 In this research we have dealt with the number of customers (cars) arrive at Periodic vehicles Inspection (PVI) company in Erbil city according to poisson process, service time follows an exponential distribution and the number of cars that require ...
Bestun Merza Abdul-Kareem +1 more
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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
openaire +4 more sources
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry [PDF]
, 2016 A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$.
Decreusefond, Laurent +2 more
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Compositions of Poisson and Gamma processes
Modern Stochastics: Theory and Applications, 2017 In the paper we study the models of time-changed Poisson and Skellam-type processes, where the role of time is played by compound Poisson-Gamma subordinators and their inverse (or first passage time) processes.
Khrystyna Buchak, Lyudmyla Sakhno
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Variance Gamma (nonlocal) equations
Modern Stochastics: Theory and Applications, 2023 Some equations are provided for the Variance Gamma process using the definition other than that based on a time-changed Brownian motion. A new nonlocal equation is obtained involving generalized Weyl derivatives, which is true even in the drifted case ...
Fausto Colantoni
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Estimating the COGARCH(1,1) model - a first go [PDF]
, 2005 We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent.
Haug, Stephan +3 more
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The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics [PDF]
, 2012 We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson.
A. Ferguson +42 more
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