They cover estimating functions for diffusion-type processes, the econometrics of high-frequency data, statistics and high-frequency data, important sampling techniques for estimating diffusion models, the non-parametric estimation of the coefficients of ergodic diffusion processes based on high-frequency data, Ornstein-Uhlenbeck related models drive by Levy processes, and parameter estimation for multiscale diffusion.

The topics include fractional Brownian motion and related processes, parametric estimation for fractional Ornstein-Uhlenbeck type processes, sequential inference and non-parametric inference for processes driven by fractional Brownian motion, parametric estimation for processes driven by a fractional Browning sheet, and self-similarity index estimation.

Characterizing the instantaneous investment opportunity set by the real interest rate and the maximum Sharpe ratio, Brennan, Wang, and Xia posit a simple model of time-varying investment opportunities in which these two variables follow correlated Ornstein-Uhlenbeck processes.

We assume the short interest rate, which is the only state variable, is given by the following stochastic differential equation: [Mathematical Expression Omitted], yielding the Ornstein-Uhlenbeck process, where m, q, and v are non-negative constants interpretable as the long-range mean to which [r.

They cover heuristics and history, probabilistic preliminaries, Feynman-Kac formulae, Gibbs measures associated with Feynman-Kac semigroups, the free Euclidean quantum field and Ornstein-Uhlenbeck processes, the Nelson model by path measures, and the Pauli-Feirz model by path measures.

The text covers the elliptic equation and the Cauchy problem under certain conditions, one-dimensional theory, uniqueness results, conservation of probability and maximum principles, properties of {T(t)} in spaces of continuous functions, uniform estimates for the derivatives of {T(t)}, point-wise estimates for the derivatives of {T(t)}, certain invariant measures in semigroups, the Ornstein-Uhlenbeck operator, a class of nonanalytic Markov semigroups, the Cauchy-Dirichlet problem, the Cauchy-Newman problem in the convex and nonconvex case, and a class of Markov semigroups associated with degenerate elliptic operators.

We particularize the case of a stochastic volatility that evolves according to an Ornstein-Uhlenbeck process, as introduced in Scott (1987) and Stein and Stein (1991): d[[sigma].