Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics, 113)
by Steven Shreve, Ioannis Karatzas
Graduate text establishing the mathematical foundations of Brownian motion, stochastic integration, and Itô calculus with applications to martingales and PDEs.
About This Book
This text presents the core theory of Brownian motion and stochastic calculus at the graduate level.
It develops the necessary measure-theoretic probability background and constructs Brownian motion rigorously.
The book covers stochastic integration, Itô’s formula, and the associated differential equations.
Applications to martingale theory and partial differential equations are included throughout.
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