Stochastic Calculus and Differential Equations for Physics and Finance

Contents; Abbreviations; Introduction; 1 Random variables and probability distributions; 1.1 Particle descriptions of partial differential equations; 1.2 Random variables and stochastic processes; 1.3 The n-point probability distributions; 1.4 Simple averages and scaling; 1.5 Pair correlations and 2-point densities; 1.6 Conditional probability densities; 1.7 Statistical ensembles and time series; 1.8 When are pair correlations enough to identify a stochastic process?; Additional reading; Exercises; 2 Martingales, Markov, and nonstationarity; 2.1 Statistically independent increments