A User's Guide to Measure Theoretic Probability

摘要: Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb beyond what they might learned in typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for mixed audience graduate undergraduate students who not had luxury taking theory. The core covers basic topics independence, conditioning, martingales, convergence distribution, Fourier transforms. In addition there are numerous sections treating traditionally thought as more advanced, such coupling KMT strong approximation, option pricing via equivalent martingale measure, isoperimetric inequality Gaussian processes. is just presentation mathematical theory, but also discussion why that takes its current form. It will be secure starting point anyone needs invoke rigorous arguments understand mean.