3 Stochastics

John von Neumann, randomly playing		Randomness, controlled

• 3.1 Equidistribution
  • 3.1.1 Linear Congruential Generators
  • 3.1.2 Shift Register Generators
  
  
• 3.2 Other Distributions
  • 3.2.1 Transformation of probability densities
  • 3.2.2 Transformation Method
  • 3.2.3 Generalized Transformation Method
  • 3.2.4 Rejection Method
  • 3.2.5 Multivariate Gaussian Distribution
  • 3.2.6 Homogeneous distributions in Orientation Space
  
  
• 3.3 Random Sequences
  • 3.3.1 Basics
  • 3.3.2 Generating a stationary Gaussian Markov sequence
  • 3.3.3 Wiener-Lévy Process (Unbiased Random Walk)
  • 3.3.4 Markov Chains (Biased Random Walk)
  • 3.3.5 Monte Carlo Method
  
  
• 3.4 Stochastic Optimization
  • 3.4.1 Simulated Annealing
  • 3.4.2 Genetic Algorithms