Stochastic Processes

This book introduces the theory of stochastic processes with applications taken from physics and finance. It includes a discussion of extreme events, ranging from their mathematical definition to their importance for financial crashes.

Contains a careful treatment of Levy processes Displays classical and modern examples for the application of stochastic processes Introduces stochastic processes in finance for natural scientists Presents the physicists view on financial markets Discusses econophysics of financial crashes Includes supplementary material: sn.pub/extras

Inhalt
A First Glimpse of Stochastic Processes.- A Brief Survey of the Mathematics of Probability Theory.- Diffusion Processes.- Beyond the Central Limit Theorem: Lévy Distributions.- Modeling the Financial Market.- Stable Distributions Revisited.- Hyperspherical Polar Coordinates.- The Weierstrass Random Walk Revisited.- The Exponentially Truncated Lévy Flight.- PutCall Parity.- Geometric Brownian Motion.