Functional limit theorems for power series with rapid decay of moving averages of Hermite processes

We aim to obtain a homogenization theorem for a passive tracer interacting with a fractional, possibly non-Gaussian, noise. To do so, we analyze limit theorems for normalized functionals of Hermite–Volterra processes and extend existing results to cover power series with fast decaying coefficients. We obtain either convergence to a Wiener process, in the short-range dependent case, or to a Hermite process, in the long-range dependent case. Furthermore, we prove convergence in the multivariate case with both, short- and long-range dependent components. Applying this theorem, we obtain a homogenization result for a slow/fast system driven by such Hermite noises.

Semantic Distributed Data for Vehicular Networks Using the Inter-Planetary File System

Vehicular networks provide means to distribute data among intelligent vehicles, increasing their efficiency and the safety of their occupants. While connected to these networks, vehicles have access to various kinds of information shared by other vehicles and road-side units (RSUs). This information includes helpful resources, such as traffic state or remote sensors. An efficient and fast system to get access to this information is important but unproductive if the data are not appropriately structured, accessible, and easy to process. This paper proposes the creation of a semantic distributed network using content-addressed networking and peer-to-peer (P2P) connections. In this open and collaborative network, RSUs and vehicles use ontologies to semantically represent information and facilitate the development of intelligent autonomous agents capable of navigating and processing the shared data. In order to create this P2P network, this paper makes use of the Inter-Planetary File System (IPFS), an open source solution that provides secure, reliable, and efficient content-addressed distributed storage over standard IP networks using the new QUIC protocol. This paper highlights the feasibility of this proposal and compares it with the state-of-the-art. Results show that IPFS is a promising technology that offers a great balance between functionality, performance, and security.

Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump

In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of them are periodic or almost periodic. Therefore, the Poisson term needs to be processed, and a new averaged equation needs to be given. For this reason, the existence of time-dependent evolution family of measures associated with the fast equation is studied and proved that it is almost periodic. Next, according to the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, the validity of the averaging principle is verified by using the Khasminskii method.