Ambit Processes Research Articles

Channel Modeling for Wireless Communications Using Ambit Processes

Developing accurate and computationally efficient channel models for mobile wireless channels poses a formidable challenge, primarily due to the highly dynamic nature of such environments and the involvement of a large number of modeling parameters. In this paper, we propose a novel geometrical model to simulate mobile wireless channels based on a framework developed from the theory of ambit processes . Under reasonable assumptions, the underlying mathematical structure of the proposed channel model enables the characterization of mobile wireless channels in terms of fading statistics, spatio-temporal channel correlation, and Doppler spectrum, besides ensuring tractable analysis. Using the ambit process model, we develop an algorithm that enables fast simulation of macro-cellular channels and accounts for key features of such channels including the appearance and disappearance of multi-path components, spatial consistency, and further captures the correlation between time-evolving delay and Doppler associated with multi-path components. Finally, we simulate macro-cellular channels using the proposed algorithm to obtain crucial insights about the channel characteristics. Numerical results indicate that the proposed channel modeling approach serves as a fairly accurate and computationally efficient design framework for wireless communication systems.

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination

Forecasting Energy Market Contracts by Ambit Processes: Empirical Study and Numerical Results.

In the present paper we exploit the theory of ambit processes to develop a model which is able to effectively forecast prices of forward contracts written on the Italian energy market. Both short-term and medium-term scenarios are considered and proper calibration procedures as well as related numerical results are provided showing a high grade of accuracy in the obtained approximations when compared with empirical time series of interest.

A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow

We discuss continuous cascade models and their potential for modelling the energy dissipation in a turbulent flow. Continuous cascade processes, expressed in terms of stochastic integrals with respect to Lévy bases, are examples of ambit processes. These models are known to reproduce experimentally observed properties of turbulence: the scaling and self-scaling of the correlators of the energy dissipation and of the moments of the coarse-grained energy dissipation. We compare three models: a normal model, a normal inverse Gaussian model, and a stable model. We show that the normal inverse Gaussian model is superior to both, the normal and the stable models, in terms of reproducing the distribution of the energy dissipation; and that the normal inverse Gaussian model is superior to the normal model and competitive with the stable model in terms of reproducing the self-scaling exponents. Furthermore, we show that the presented analysis is parsimonious in the sense that the self-scaling exponents are predicted from the one-point distribution of the energy dissipation, and that the shape of these distributions is independent of the Reynolds number.

New Central Limit Theorems for Functionals of Gaussian Processes and their Applications

As a consequence of the seminal work of Nualart and Peccati in 2005 we have new central limit theorems for functional of Gaussian processes that have allowed us to elucidate the asymptotic behavior of the multipower variation of certain ambit processes, see Barndorff-Nielsen et al. (2009c). This survey intends to explain the role of the Malliavin calculus to reach these results.

Modelling Energy Spot Prices by Lévy Semistationary Processes

This paper introduces a new modelling framework for energy spot prices based on Levy semistationary processes. Levy semistationary processes are special cases of the general class of ambit processes. We provide a detailed analysis of the probabilistic properties of such models and we show how they are able to capture many of the stylised facts observed in energy markets. Furthermore, we derive forward prices based on our spot price model. As it turns out, many of the classical spot models can be embedded into our novel modelling framework.

Ambit Processes and Stochastic Partial Differential Equations

Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Levy noise analysis.