共查询到20条相似文献,搜索用时 15 毫秒
1.
The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NHSTFPP). We compute their pmf and generating function and investigate the associated differential equation. The limit theorems for the NHSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NHTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NHTFPP. We investigate the limit theorem for the fractional non-homogeneous Poisson process (FNHPP) studied by Leonenko et al. (2014). Finally, we present some simulated sample paths of the NHSTFPP process. 相似文献
2.
In this paper, we introduce a space fractional negative binomial process (SFNB) by time-changing the space fractional Poisson process by a gamma subordinator. Its one-dimensional distributions are derived in terms of generalized Wright functions and their governing equations are obtained. It is a Lévy process and the corresponding Lévy measure is given. Extensions to the case of distributed order SFNB, where the fractional index follows a two-point distribution, are investigated in detail. The relationship with space fractional Polya-type processes is also discussed. Moreover, we define and study multivariate versions, which we obtain by time-changing a d-dimensional space-fractional Poisson process by a common independent gamma subordinator. Some applications to population’s growth and epidemiology models are explored. Finally, we discuss algorithms for the simulation of the SFNB process. 相似文献
3.
Juan José Víquez R 《随机分析与应用》2018,36(2):341-372
We prove the chain rule in the more general framework of the Wiener–Poisson space, allowing us to obtain the so-called Nourdin–Peccati bound. From this bound, we obtain a second-order Poincaré-type inequality that is useful in terms of computations. For completeness we survey these results on the Wiener space, the Poisson space, and the Wiener–Poisson space. We also give several applications to central limit theorems with relevant examples: linear functionals of Gaussian subordinated fields (where the subordinated field can be processes like fractional Brownian motion or the solution of the Ornstein–Uhlenbeck SDE driven by fractional Brownian motion), Poisson functionals in the first Poisson chaos restricted to infinitely many “small” jumps (particularly fractional Lévy processes), and the product of two Ornstein–Uhlenbeck processes (one in the Wiener space and the other in the Poisson space). We also obtain bounds for their rate of convergence to normality. 相似文献
4.
Fractional Poisson process 总被引:1,自引:0,他引:1
A fractional non-Markov Poisson stochastic process has been developed based on fractional generalization of the Kolmogorov–Feller equation. We have found the probability of n arrivals by time t for fractional stream of events. The fractional Poisson process captures long-memory effect which results in non-exponential waiting time distribution empirically observed in complex systems. In comparison with the standard Poisson process the developed model includes additional parameter μ. At μ=1 the fractional Poisson becomes the standard Poisson and we reproduce the well known results related to the standard Poisson process.As an application of developed fractional stochastic model we have introduced and elaborated fractional compound Poisson process. 相似文献
5.
本文研究了以分数布朗运动为输入过程的存储过程上穿高水平u形成的点过程的渐近泊松特性,结果表明当分数布朗运动参数H∈(0,1/2),u→∞时,该点过程弱收敛到泊松过程. 相似文献
6.
We prove that in the Euclidean space of arbitrary dimension the inversion of the isotropic stable Lévy process killed at the origin is, after an appropriate change of time, the same stable process conditioned in the sense of Doob by the Riesz kernel. Using this identification we derive and explain transformation rules for the Kelvin transform acting on the Green function and the Poisson kernel of the stable process and on solutions of Schr?dinger equation based on the fractional Laplacian. The Brownian motion and the classical Laplacian are included as a special case. 相似文献
7.
Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space \(\mathbb{R}_+^2\). Some properties are given and, in particular, we prove a long-range dependence property. 相似文献
8.
Vicky Fasen 《Queueing Systems》2010,66(4):313-350
We consider a cluster Poisson model with heavy-tailed interarrival times and cluster sizes as a generalization of an infinite
source Poisson model where the file sizes have a regularly varying tail distribution function or a finite second moment. One
result is that this model reflects long-range dependence of teletraffic data. We show that depending on the heaviness of the
file sizes, the interarrival times and the cluster sizes we have to distinguish different growths rates for the time scale
of the cumulative traffic. The mean corrected cumulative input process converges to a fractional Brownian motion in the fast
growth case. However, in the intermediate and the slow growth case we can have convergence to a stable Lévy motion or a fractional
Brownian motion as well depending on the heaviness of the underlying distributions. These results are contrary to the idea
that cumulative broadband network traffic converges in the slow growth case to a stable process. Furthermore, we derive the
asymptotic behavior of the cluster Poisson point process which models the arrival times of data packets and the individual
input process itself. 相似文献
9.
Journal of Theoretical Probability - In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence property. It is proved by establishing an asymptotic... 相似文献
10.
Dexter O. Cahoy Federico Polito 《Communications in Nonlinear Science & Numerical Simulation》2013,18(3):639-650
The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized the standard and fractional Poisson processes through the waiting time distribution, and showed their relations to an integral operator with a generalized Mittag–Leffler function in the kernel. The waiting times of the proposed renewal processes have the generalized Mittag–Leffler and stretched–squashed Mittag–Leffler distributions. Note that the generalizations naturally provide greater flexibility in modeling real-life renewal processes. Algorithms to simulate sample paths and to estimate the model parameters are derived. Note also that these procedures are necessary to make these models more usable in practice. State probabilities and other qualitative or quantitative features of the models are also discussed. 相似文献
11.
假设股票价格遵循分数布朗运动和复合泊松过程驱动的随机微分方程,短期利率服从HullWhite模型,建立了随机利率情形下的分数跳-扩散Ornstein-Uhlenbeck期权定价模型,利用价格过程的实际概率测度和公平保费原理,得到了欧式看涨期权定价的解析表达式,推广了Black-Scholes模型. 相似文献
12.
Yoshihiro Mizuta 《Potential Analysis》2006,25(1):29-36
Our aim in this paper is to prove the existence of tangential limits for Poisson integrals of the fractional order of functions in the L p Hölder space on half spaces. 相似文献
13.
14.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3425-3430
This paper discusses method-of-moments estimators for parameters in the fractional compound Poisson process and establishes asymptotic normality of estimators. Simulation are presented to illustrate the properties of the estimators. 相似文献
15.
In this paper we focus on networks of infinite-server queues with nonhomogeneous Poisson arrival processes. We start by introducing a more general Poisson-arrival-location model (PALM) in which arrivals move independently through a general state space according to a location stochastic process after arriving according to a nonhomogeneous Poisson process. The usual open network of infinite-server queues, which is also known as a linear population process or a linear stochastic compartmental model, arises in the special case of a finite state space. The mathematical foundation is a Poisson-random-measure representation, which can be obtained by stochastic integration. It implies a time-dependent product-form result: For appropriate initial conditions, the queue lengths (numbers of customers in disjoint subsets of the state space) at any time are independent Poisson random variables. Even though there is no dependence among the queue lengths at each time, there is important dependence among the queue lengths at different times. We show that the joint distribution is multivariate Poisson, and calculate the covariances. A unified framework for constructing stochastic processes of interest is provided by stochastically integrating various functionals of the location process with respect to the Poisson arrival process. We use this approach to study the flows in the queueing network; e.g., we show that the aggregate arrival and departure processes at a given queue (to and from other queues as well as outside the network) are generalized Poisson processes (without necessarily having a rate or unit jumps) if and only if no customer can visit that queue more than once. We also characterize the aggregate arrival and departure processes when customers can visit the queues more frequently. In addition to obtaining structural results, we use the stochastic integrals to obtain explicit expressions for time-dependent means and covariances. We do this in two ways. First, we decompose the entire network into a superposition of independent networks with fixed deterministic routes. Second, we make Markov assumptions, initially for the evolution of the routes and finally for the entire location process. For Markov routing among the queues, the aggregate arrival rates are obtained as the solution to a system of input equations, which have a unique solution under appropriate qualifications, but not in general. Linear ordinary differential equations characterize the time-dependent means and covariances in the totally Markovian case. 相似文献
16.
The stable Telecom process has infinite variance and appears as a limit of renormalized renewal reward processes. We study its Poissonized version where the infinite variance stable measure is replaced by a Poisson point measure. We show that this Poissonized version converges to the stable Telecom process at small scales and to the Gaussian fractional Brownian motion at large scales. This process is therefore locally as well as asymptotically self-similar. The value of the self-similarity parameter at large scales, namely the self-similarity parameter of the limit fractional Brownian motion, depends on the form the Poissonized Telecom process. The Poissonized Telecom process is a Poissonized mixed moving average. We investigate more general Poissonized mixed moving averages as well. 相似文献
17.
The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type of characterization for the fractional powers of second order partial differential operators in some class. We also get a Poisson formula and a system of Cauchy–Riemann equations for the extension. The method is applied to the fractional harmonic oscillator H σ = (? Δ + |x|2)σ to deduce a Harnack's inequality. A pointwise formula for H σ f(x) and some maximum and comparison principles are derived. 相似文献
18.
We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space. 相似文献
19.
We consider the Cauchy problem for an abstract Euler–Poisson–Darboux equation in a Banach space and prove a necessary and a sufficient condition for the solvability of this problem. The conditions are stated in terms of an estimate for the norm of a fractional power of the resolvent and its derivatives. The properties of solutions are established, and examples are given. 相似文献
20.
David R. Brillinger 《Stochastic Processes and their Applications》1978,6(2):135-137
The Gauss-Poisson (G-P) process introduced in Newman [3] and discussed in Milne and Westcott [2] is represented as the superposition of the marginal processes of a Poisson process defined on the product space X × X and an independent Poisson process on X. This representation explains directly many of the properties of the G-P process and indicates a means of simulating its realizations. 相似文献