Ebook: Infinitely Divisible Statistical Experiments

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Content:
Front Matter....Pages N2-VI
Introduction....Pages 1-13
Basic Concepts....Pages 14-18
Gaussian Experiments....Pages 19-24
Introduction to Poisson Experiments....Pages 25-31
Convergence of Poisson Experiments....Pages 32-37
Convergence of Triangular Arrays....Pages 38-46
Identification of Limit Experiments....Pages 47-54
Preliminaries....Pages 55-57
Infinitely Divisible Probability Measures....Pages 58-62
The L?vy-Khintchine Formula for Standard Measures....Pages 63-88
The L?vy-Khintchine Formula for Arbitrary Regular Infinitely Divisible Statistical Experiments....Pages 89-105
Generalized Poisson Processes....Pages 106-110
Standard Poisson Experiments....Pages 111-123
Preliminaries....Pages 124-125
Experiments with Independent Increments....Pages 126-129
Existence and Construction of Experiments with Independent Increments....Pages 130-132
Infinitely Divisible Experiments with Independent Increments....Pages 133-139
Weak Convergence of Triangular Arrays to Experiments with Independent Increments....Pages 140-143
The Likelihood Process....Pages 144-148
Application to Densities with Jumps....Pages 149-153
Back Matter....Pages 154-165

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Content:
Front Matter....Pages N2-VI
Introduction....Pages 1-13
Basic Concepts....Pages 14-18
Gaussian Experiments....Pages 19-24
Introduction to Poisson Experiments....Pages 25-31
Convergence of Poisson Experiments....Pages 32-37
Convergence of Triangular Arrays....Pages 38-46
Identification of Limit Experiments....Pages 47-54
Preliminaries....Pages 55-57
Infinitely Divisible Probability Measures....Pages 58-62
The L?vy-Khintchine Formula for Standard Measures....Pages 63-88
The L?vy-Khintchine Formula for Arbitrary Regular Infinitely Divisible Statistical Experiments....Pages 89-105
Generalized Poisson Processes....Pages 106-110
Standard Poisson Experiments....Pages 111-123
Preliminaries....Pages 124-125
Experiments with Independent Increments....Pages 126-129
Existence and Construction of Experiments with Independent Increments....Pages 130-132
Infinitely Divisible Experiments with Independent Increments....Pages 133-139
Weak Convergence of Triangular Arrays to Experiments with Independent Increments....Pages 140-143
The Likelihood Process....Pages 144-148
Application to Densities with Jumps....Pages 149-153
Back Matter....Pages 154-165
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