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


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Table of Contents

1. Introduction.- 2. Preliminaries.- 3. Estimation of the Parameters.- 4. Simulation Algorithms and Simulation Studies.- 5. Proofs of all the results.- A. Complementary Results.- A.1. Introduction.- A.2. Proofs.- B. Tables and Figures Related to the Simulation Studies.- C. Some Pascal Procedures and Functions.- References.- Index.

About the Author

Corinne Berzin received a degree of "Agrégation de mathématiques" from Lille University, Lille, France, in 1985. She got her Ph.D. degree in 1989 from Université Paris-Sud, Orsay, France, under the supervision of D. Dacunha-Castelle and M. Wschebor. From 1990 to 1999, she was Assistant Professor at Université de Versailles Saint-Quentin-en-Yvelines, France. Since 1999, as Professor of Mathematics, she affiliated to Université de Grenoble Alpes and is a researcher of the IPS team at Laboratoire Jean-Kuntzmann (Grenoble, France). Her research interests are focused on random fields, crossings and local time, density estimation, estimation in stochastic differential equations driven by fractional Brownian motion.

Alain Latour got his Ph.D. in computer science from Université de Montréal in 1986.He started his career at Université du Québec à Montréal (UQÀM) were he was full professor at the Department of Mathematics. During many years he was responsible for the Statistics group of this department and Director of the Data Analysis Consulting Service. He definitively left Montreal for Grenoble in 2005 but is still Associated professor at UQÀM. He remains associated researcher in the Applied Stochastic Modeling Team at UQÀM. Now, he his affiliated to Université de Grenoble Alpes and researcher of the IPS team at Laboratoire Jean-Kuntzmann (Grenoble, France). He is mainly interested in estimation problems and modeling of stochastic processes and in data analysi

s in general.

José R. León got his Ph.D. in 1983 under the supervision of M. Wschebor. He is full professor at Escuela de Matemática - Facultad de Ciencias, Universidad Central de Venezuela and corresponding member of the Academia de Ciencias Físicas, Matemáticas y Naturales de Venezuela. Professor Le'on has been invited professor and researcher in many different French universities. He has many articles in international journals and reviews. He supervised several Ph.D. and Master thesis in Venezuela and France. His research interests are focused on the estimation for Gaussian processes and also on non-parametric estimation in stochastic processes.


“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)

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