Statiscal Methods for Stochastic Differential Equations

Estimating functions for diffusion-type processes, Michael Sørensen
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 Lévy processes, Peter J. Brockwell and Alexander Lindner
Introduction
Lévy 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