Semimartingales and Their Statistical Inference

Abstract

Semimartingales Introduction Stochastic Processes Doob-Meyer Decomposition Stochastic Integration Local Martingales Semimartingales Girsanov's Theorem Limit Theorems for Semimartingales Diffusion Type Processes Point Processes Exponential Families of Stochastic Processes Introduction Exponential Families of Semimartingales Stochastic Time Transformation Asymptotic Likelihood Theory Introduction Examples Asymptotic Likelihood Theory for a Class of Exponential Families of Semimartingales Asymptotic Likelihood Theory for General Processes Exercises Asymptotic Likelihood Theory for Diffusion Processes with Jumps Introduction Absolute Continuity for Measures Generated by Diffusions with Jumps Score Vector and Information Matrix Asymptotic Likelihood Theory for Diffusion Processes with Jumps Asymptotic Likelihood Theory for Exponential Families Examples Exercises Quasi-likelihood and Semimartingales Quasi-Likelihood and Discrete Time Processes Quasi-Likelihood and Continuous Time Processes Quasi-Likelihood and Special Semimartingales Quasi-Likelihood and Partially Specified Counting Processes Examples Exercises Local Asymptotic Behavior of Semimartingales Experiments Locally Asymptotic Mixed Normality Locally Asymptotic Quadraticity Locally Asymptotic Infinite Divisibility Locally Asymptotic Normality (Infinite Dimensional Parameter Case) Multiplicative Models and Asymptotic Variance Bounds Exercises Likelihood and Asymptotic Efficiency Fully Specified Likelihood (Factorisable Models) Partially Specified Likelihood Partial Likelihood and Asymptotic Efficiency Partially Specified Likelihood and Asymptotic Efficiency Inference for Counting Processes Introduction Parametric Inference for Counting Processes Semiparametric Inference for Counting Processes Nonparametric Inference for Counting Processes Inference for Additive-Multiplicative Hazard Models Inference for Semimartingale Regression Models Estimation by the Quasi-Least-Squares Method Estimation by the Maximum Likelihood Method Estimation by the Method of Sieves Nonlinear Semimartingale Regression Models Applications to Stochastic Modeling Introduction Applications to Engineering and Economic Systems Applications to Modeling of Neuron Movement in Nervous Systems Appendix Doleans Measure for Semimartingales and Burkholder's Inequality for Martingales Interchanging Stochastic Integration and Ordinary Differentiation and Fubini-Type Theorem for Stochastic Integrals The Fundamental Identity of the Sequential Analysis Stieltjes-Lebesgue Calculus A Useful Lemma Contiguity Notes References

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