Baldi P. Stochastic Calculus: An Introduction Through Theory and Exercises

Springer International Publishing AG, 2017. — 632 p. — (Universitext) — ISBN: 978-3-319-62225-5.Courses in Stochastic Calculus have in the last two decades changed their target audience. Once this advanced part of mathematics was of interest mainly to postgraduates intending to pursue an academic research career, but now many professionals cannot do without the ability to manipulate stochastic models.
The aim of this book is to provide a tool in this direction, starting from a basic probability background (with measure theory, however). The intended audience should, moreover, have serious mathematical bases. The entire content of this book should provide material for a two-semester class. My experience is that Chaps. 2–9 provide the material for a course of 72 h, including the time devoted to the exercises.Elements of Probability
Stochastic Processes
Brownian Motion
Conditional Probability
Martingales
Markov Processes
The Stochastic Integral
Stochastic Calculus
Stochastic Differential Equations
PDE Problems and Diffusions
Simulation
Back to Stochastic Calculus
An Application: Finance