Brownian Motion, Martingales, and Stochastic Calculus

• Main Author: Le Gall, Jean-François (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Graduate Texts in Mathematics, 274
• Subjects: Mathematics.; Measure theory.; Economics, Mathematical.; System theory.; Mathematical models.; Probabilities.; Probability Theory and Stochastic Processes.; Quantitative Finance.; Measure and Integration.; Mathematical Modeling and Industrial Mathematics.; Systems Theory, Control.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated...

Table of Contents:

• Gaussian variables and Gaussian processes
• Brownian motion
• Filtrations and martingales
• Continuous semimartingales
• Stochastic integration
• General theory of Markov processes
• Brownian motion and partial differential equations
• Stochastic differential equations
• Local times
• The monotone class lemma
• Discrete martingales
• References.