1,721,114 research outputs found
Multifractal products of stationary diffusion processes
No full textWe investigate the properties of multifractal products of the exponential of stationary diffusion processes defined by stochastic differential equations with linear drift and certain form of the diffusion coefficient corresponding to a variety of marginal distributions. The conditions on the mean, variance and covariance functions of these processes are interpreted in terms of the moment generating functions. We provide three illustrative examples of normal, gamma and beta distributions. We establish the corresponding lognormal, log-gamma and log-beta scenarios for the limiting processes, including their Rényi functions and dependence structure
Multifractality of products of geometric Ornstein-Uhlenbeck -type processes
Get PDFWe investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure
Simulation of multifractal products of Ornstein-Uhlenbeck type processes
No full textThis paper investigates and provides evidence of the multifractal properties of products of the exponential of Ornstein–Uhlenbeck processes driven by Lévy motion. We demonstrate in detail the construction of a multifractal process with gamma subordinator as the background driving Lévy process. Simulations are performed for the scenarios corresponding to the normal inverse Gaussian, gamma and inverse Gaussian distributions. The log periodograms and Rényi functions of the simulated processes are also computed to investigate their multifractality
Fractional spherical random fields
Full text linkIn this paper we study the solutions of different forms of fractional equations on the unit sphere S21 ⊂R3 possessing the structure of time-dependent random fields. We study the correlation functions of the random fields emerging in the analysis of the solutions of the fractional equations and examine their long-range behaviour
Fractional Erlang queues
Full text linkWe introduce a fractional generalization of the Erlang Queues M∕Ek∕1. Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward equation for such process, then we use such equation to obtain an interpretation of this process in the queuing theory context. Then we also exploit the transient state probabilities and some features of this fractional queue model, such as the mean queue length, the distribution of the busy periods and some conditional distributions of the waiting times. Finally, we provide some algorithms to simulate their sample paths
Fractional queues with catastrophes and their transient behaviour
Full text linkStarting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrophes. In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role. We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem. Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe
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