12General Lévy Processes
12.1 Introduction and Definitions
In this chapter we give basic definitions concerning stochastic processes and Lévy processes and present the main properties and examples of the Lévy stochastic processes. We will conclude this chapter with an introduction to the range scale analysis and detrended fluctuation analysis (DFA). The range scale analysis and DFA are very important methodologies that can be used to analyze extreme events, like financial crashes and earthquakes.
12.2 Lévy Processes
Stochastic Lévy processes play a fundamental role in mathematical finance and in other fields such as physics (turbulence), engineering (telecommunications and dams), actuarial science (insurance risk), and several others. References on stochastic processes and Lévy processes can be found in [8, 21, 159, 177, 179, 180, 200].
We recall the definition of stochastic processes which was previously defined in Chapter 1 of this book.
Get Quantitative Finance now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
