Preface -- Notation -- Stochastic Processes and Stochastic Differential Equations -- Elements of probability and random variables -- Mean, variance, and moments -- Change of measure and Radon-Nikodým derivative -- Random number generation -- The Monte Carlo method -- Variance reduction techniques -- Preferential sampling -- Control variables -- Antithetic sampling -- Generalities of stochastic processes -- Filtrations -- Simple and quadratic variation of a process -- Moments, covariance, and increments of stochastic processes -- Conditional expectation -- Martingales -- Brownian motion -- Brownian motion as the limit of a random walk -- Brownian motion as L2[0,T] expansion -- Brownian motion paths are nowhere differentiable -- Geometric Brownian motion -- Brownian bridge -- Stochastic integrals and stochastic differential equations -- Properties of the stochastic integral and Itô processes -- Diffusion processes -- Ergodicity -- Markovianity -- Quadratic variation -- Infinitesimal generator of a diffusion process -- How to obtain a martingale from a diffusion process -- Itô formula -- Orders of differentials in the Itô formula -- Linear stochastic differential equations -- Derivation of the SDE for the geometric Brownian motion -- The Lamperti transform -- Girsanov's theorem and likelihood ratio for diffusion processes -- Some parametric families of stochastic processes -- Ornstein-Uhlenbeck or Vasicek process -- The Black-Scholes-Merton or geometric Brownian motion model -- The Cox-Ingersoll-Ross model -- The CKLS family of models -- The modified CIR and hyperbolic processes -- The hyperbolic processes -- The nonlinear mean reversion Aït-Sahalia model -- Double-well potential -- The Jacobi diffusion process -- Ahn and Gao model or inverse of Feller's square root model -- Radial Ornstein-Uhlenbeck process -- Pearson diffusions.

Another classification of linear stochastic systems -- One epidemic model -- The stochastic cusp catastrophe model -- Exponential families of diffusions -- Generalized inverse gaussian diffusions -- Numerical Methods for SDE -- Euler approximation -- A note on code vectorization -- Milstein scheme -- Relationship between Milstein and Euler schemes -- Transform of the geometric Brownian motion -- Transform of the Cox-Ingersoll-Ross process -- Implementation of Euler and Milstein schemes: the sde.sim function -- Example of use -- The constant elasticity of variance process and strange paths -- Predictor-corrector method -- Strong convergence for Euler and Milstein schemes -- KPS method of strong order =1.5 -- Second Milstein scheme -- Drawing from the transition density -- The Ornstein-Uhlenbeck or Vasicek process -- The Black and Scholes process -- The CIR process -- Drawing from one model of the previous classes -- Local linearization method -- The Ozaki method -- The Shoji-Ozaki method -- Exact sampling -- Simulation of diffusion bridges -- The algorithm -- Numerical considerations about the Euler scheme -- Variance reduction techniques -- Control variables -- Summary of the function sde.sim -- Tips and tricks on simulation -- Parametric Estimation -- Exact likelihood inference -- The Ornstein-Uhlenbeck or Vasicek model -- The Black and Scholes or geometric Brownian motion model -- The Cox-Ingersoll-Ross model -- Pseudo-likelihood methods -- Euler method -- Elerian method -- Local linearization methods -- Comparison of pseudo-likelihoods -- Approximated likelihood methods -- Kessler method -- Simulated likelihood method -- Hermite polynomials expansion of the likelihood -- Bayesian estimation -- Estimating functions -- Simple estimating functions -- Algorithm 1 for simple estimating functions -- Algorithm 2 for simple estimating functions.

Martingale estimating functions -- Polynomial martingale estimating functions -- Estimating functions based on eigenfunctions -- Estimating functions based on transform functions -- Discretization of continuous-time estimators -- Generalized method of moments -- The GMM algorithm -- GMM, stochastic differential equations, and Euler method -- What about multidimensional diffusion processes? -- Miscellaneous Topics -- Model identification via Akaike's information criterion -- Nonparametric estimation -- Stationary density estimation -- Local-time and stationary density estimators -- Estimation of diffusion and drift coefficients -- Change-point estimation -- Estimation of the change point with unknown drift -- A famous example -- Appendix A: A brief excursus into R -- Typing into the R console -- Assignments -- R vectors and linear algebra -- Subsetting -- Different types of objects -- Expressions and functions -- Loops and vectorization -- Environments -- Time series objects -- R Scripts -- Miscellanea -- Appendix B: The sde Package -- BM -- cpoint -- DBridge -- dcElerian -- dcEuler -- dcKessler -- dcOzaki -- dcShoji -- dcSim -- DWJ -- EULERloglik -- gmm -- HPloglik -- ksmooth -- linear.mart.ef -- rcBS -- rcCIR -- rcOU -- rsCIR -- rsOU -- sde.sim -- sdeAIC -- SIMloglik -- simple.ef -- simple.ef2 -- References -- Index.