Masoliver J. Random Processes. First-passage and Escape 2018

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