Probabilities on algebraic structures

Title page
Introduction
CHAPTER 1. Historical background and practical motivation of the problem
1.1. Why study probabilities on general structures
1.2. Some classical methods and results
1.3. Practical background to the theory
1.4. Historical background
CBAPTER 2. Stochastic semi-groups
2.1. Generalities
2.2. Stochastic semi-gronps
2.3. Compact stochastic semi-groupa
2.4. Illustrations
CBAPTER 3. Stochastic groups; compact and commutative cases
3.1. Generalities on stochastic groups
3.2. Compact stochastic groups
3.3. Commutative locally compact stochastic groups
3.4. Illustrations
CHAPTER 4. Stochastic Lie groups
4.1. Preliminaries on Lie groupa
4.2. Homogeneous processes on Lie groupa
4.3. The law of large numbers for stochastic Lie groups
4.4. A central limit theorem
4.5. Illustrations
CHAPTER 5. Locally compact stochastic groups
5.1. Unitary representations
5.2. Fourier analysis of locally compact stochastic groupa
5.3. Limit theorems on locally compact stochastic groupa
5.4. Limit theorems on certain divisible groups
5.5. Illustrations
CBAPTER 6. Stochastic linear spaces
6.1. Probabilities on a Banach space
6.2. Fourier analysis in a stochastic Banach space
6.3. Normal distributions in a Hilbert space
6.4. The law of large numbers
6.5. The central limit theorem
6.6. Stochastic Schwartz distributions
6.7. Illustrations
CHAPTER 7. Stochastic algebras
7.1. Additive and multiplicative limit theorems
7.2. Probabilities on a Banach algebra
7.3. Stochastic operators and random equations
7.4. More special structures
7.5. Illustrations
Outlook
Notes
Bibliography
Index