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.
Contents: - Random Processes:
- Fundamentals of Probability
- Random Processes: Definitions and General Properties
- Markov Processes
- Diffusion Processes
- Fokker–Planck Equations in Several Dimensions
- Linear Response Theory
- Stochastic Calculus with Some Applications:
- Introduction to Stochastic Calculus
- Stochastic Differential Equations
- Some Financial Applications
- The Level Crossing Problem:
- First-Passage, Escape and Extremes. General Settings
- The Level Crossing Problem for Diffusion Processes
- First-Passage and Extremes in Socio-Economic Systems
Readership: Advanced students and professional researchers.
Random Processes;First-Passage Times;Stochastic Calculus;Extremes0
Key Features:- The book gathers some aspects that are often disseminated in several publications (books and technical reports)
- The treatment of topics is rather unique (specially those of first-passages)
