Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion

Beschreibung

This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered.It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence.The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events, and contaminant diffusion problems.
This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered.It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence.The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events and contaminant diffusion problems.
Of interest to mathematicians, engineers with basic knowledge in probability, statistics and stochastic processes Simulation Algorithms and Pascal code are available Elegance and completeness of the proofs of the theoretical results Estimation procedures are easily implemented as computer programs showing the application worth of the approach

Autor*in

Corinne Berzin

Themen in »Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion«

Asymptotic properties of estimators Fractional Brownian motion Hypothesis testing Limit theorem Non parametric estimation Stochastic integral

Stimmen zu »Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion«

“I can recommend it to statisticians, specialists in probability and, in general, any person interested in simulations and algorithms for fBm. The book mainly develops estimation techniques for the Hurst parameter H and the local variance or volatility of four models of stochastic differential equations (SDEs) driven by fractional noise.” (María J. Garrido-Atienza, Mathematical Reviews, August, 2015)

Details

Link teilen