I. Limits of Triangular Arrays of Experiments -- 1. Basic Concepts -- 2. Gaussian Experiments -- 3. Introduction to Poisson Experiments -- 4. Convergence of Poisson Experiments -- 5. Convergence of Triangular Arrays -- 6. Identification of Limit Experiments -- II. The Lévy-Khintchine Formula for Infinitely Divisible Experiments -- 7. Preliminaries -- 8. Infinitely Divisible Probability Measures -- 9. The Lévy-Khintchine Formula for Standard Measures -- 10. The Lévy-Khintchine Formula for Arbitrary Regular Infinitely Divisible Statistical Experiments -- III. Representation of Poisson Experiments -- 11. Generalized Poisson Processes -- 12. Standard Poisson Experiments -- IV. Statistical Experiments with Independent Increments -- 13. Preliminaries -- 14. Experiments with Independent Increments -- 15. Existence and Construction of Experiments with Independent Increments -- 16. Infinitely Divisible Experiments with Independent Increments -- 17. Weak Convergence of Triangular Arrays to Experiments with Independent Increments -- 18. The Likelihood Process -- 19. Application to Densities with Jumps -- List of Symbols -- Author Index.