Stochastic Calculus for Fractional Brownian Motion and Applications

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter exte

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Editors: J. Gani, C.C. Heyde, P. Jagers, T.G. Kurtz

Probability and Its Applications Anderson: Continuous-Time Markov Chains. Azencott/Dacunha-Castelle: Series of Irregular Observations. Bass: Diffusions and Elliptic Operators. Bass: Probabilistic Techniques in Analysis. Berglund/Gentz: Noise-Induced Phenomena in Slow-Fast Dynamical Systems. Biagini/Hu/Øksendal/Zhang: Stochastic Calculus for Fractional Brownian Motion and Applications. Chen: Eigenvalues, Inequalities and Ergodic Theory. Choi: ARMA Model Identification. Costa/Fragoso/Marques: Discrete-Time Markov Jump Linear Systems. Daley/Vere-Jones: An Introduction to the Theory of Point Processes Volume I: Elementary Theory and Methods, Second Edition. de la Peña/Giné: Decoupling: From Dependence to Independence. Durrett: Probability Models for DNA Sequence Evolution. Galambos/Simonelli: Bonferroni-type Inequalities with Applications. Gani (Editor): The Craft of Probabilistic Modelling. Grandell: Aspects of Risk Theory. Gut: Stopped Random Walks. Guyon: Random Fields on a Network. Kallenberg: Foundations of Modern Probability, Second Edition. Last/Brandt: Marked Point Processes on the Real Line. Leadbetter/Lindgren/Rootzén: Extremes and Related Properties of Random Sequences and Processes. Molchanov: Theory of Random Sets. Nualart: The Malliavin Calculus and Related Topics. Rachev/Rüschendorf: Mass Transportation Problems. Volume I: Theory. Rachev/Rüschendorf: Mass Transportation Problems. Volume II: Applications. Resnick: Extreme Values, Regular Variation and Point Processes. Schmidli: Stochastic Control in Insurance. Shedler: Regeneration and Networks of Queues. Silvestrov: Limit Theorems for Randomly Stopped Stochastic Processes. Thorisson: Coupling, Stationarity and Regeneration. Todorovic: An Introduction to Stochastic Processes and Their Applications.

Francesca Biagini Bernt Øksendal

Yaozhong Hu Tusheng Zhang

Stochastic Calculus for Fractional Brownian Motion and Applications

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Francesca Biagini, PhD Mathematisches Institut, LMU München Theresienstr. 39 D 80333 Munich, Germany Yaozhong Hu, PhD Department of Mathematics University of Kansas, 405 Snow Hall Lawrence, Kansas 66045-2142 USA and Center of Mathematics for Applications (CMA) Department of Mathematics University of Oslo, Box 1053 Blindern N-0316, Oslo, Norway

Bernt Øksendal, PhD Department of Mathematics University of Oslo, Box 1053 Blindern N-0316, Oslo and Norwegian School of Economics and Business Administration (NHH) Helleveien 30, N-5045, Bergen, Norway Tusheng Zhang, PhD Department of Mathematics University of Manchester, Oxford Road Manchester M13 9PL and Center of Mathematics for Applications (CMA) Department of Mathematics University of Oslo, Box 1053 Blindern N-0316, Oslo, Norway

Series Editors: J. Gani Stochastic Analysis Group, CMA Australian National University Canberra ACT 0200, Australia

P. Jagers Mathematical Statistics Chalmers University of Technology SE-412 96 Göteberg, Sweden

C.C. Heyde Stochastic Analysis Group, CMA Australian National University Canberra ACT 0200