Textbook in PDF format

Random processes are one of the most powerful tools in the study and understanding of countless phenomena in natural and social sciences.The book is a complete medium-level introduction to the subject. The book is written in a clear and pedagogical manner but with enough rigor and scope that can appeal to both students and researchers.This book is addressed to advanced students and professional researchers in many branches of science where level crossings and extremes appear but with some particular emphasis on some applications in socio-economic systems. Fundamentals of probability Random processes : definitions and general properties Markov processes Diffusion processes Fokker-planck equations in several dimensions Linear response theory Introduction to stochastic calculus Stochastic differential equations Some financial applications First-passage, escape and extremes The level crossing problem for difusion processes First-passage and extremes in socio-economic systems