Statistical methods for stochastic differential equations
- Boca Raton, FL : CRC Press, c2012.
- Physical description
- xxiv, 483 p. : ill. ; 24 cm.
- Monographs on statistics and applied probability (Series) 124.
QA274.23 .S75 2012
- Unknown QA274.23 .S75 2012
- Includes bibliographical references and index.
- Estimating functions for diffusion-type processes, Michael Sorensen Introduction Low frequency asymptotics Martingale estimating functions The likelihood function Non-martingale estimating functions High-frequency asymptotics High-frequency asymptotics in a fixed time-interval Small-diffusion asymptotics Non-Markovian models General asymptotic results for estimating functions Optimal estimating functions: General theory The econometrics of high frequency data, Per. A. Mykland and Lan Zhang Introduction Time varying drift and volatility Behavior of estimators: Variance Asymptotic normality Microstructure Methods based on contiguity Irregularly spaced data Statistics and high frequency data, Jean Jacod Introduction What can be estimated? Wiener plus compound Poisson processes Auxiliary limit theorems A first LNN (Law of Large Numbers) Some other LNNs A first CLT CLT with discontinuous limits Estimation of the integrated volatility Testing for jumps Testing for common jumps The Blumenthal-Getoor index Importance sampling techniques for estimation of diffusion models, Omiros Papaspiliopoulos and Gareth Roberts Overview of the chapter Background IS estimators based on bridge processes IS estimators based on guided processes Unbiased Monte Carlo for diffusions Appendix: Typical problems of the projection-simulation paradigm in MC for diffusions Appendix: Gaussian change of measure Non parametric estimation of the coefficients of ergodic diffusion processes based on high frequency data, Fabienne Comte, Valentine Genon-Catalot, and Yves Rozenholc Introduction Model and assumptions Observations and asymptotic framework Estimation method Drift estimation Diffusion coefficient estimation Examples and practical implementation Bibliographical remarks Appendix. Proof of Proposition.13 Ornstein-Uhlenbeck related models driven by Levy processes, Peter J. Brockwell and Alexander Lindner Introduction Levy processes Ornstein-Uhlenbeck related models Some estimation methods Parameter estimation for multiscale diffusions: an overview, Grigorios A. Pavliotis, Yvo Pokern, and Andrew M. Stuart Introduction Illustrative examples Averaging and homogenization Subsampling Hypoelliptic diffusions Nonparametric drift estimation Conclusions and further work.
- (source: Nielsen Book Data)
- Publisher's Summary
- The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.
(source: Nielsen Book Data)
- Publication date
- edited by Mathieu Kessler, Alexander Lindner, Michael Sørensen.
- Monographs on statistics and applied probability ; 124