Stochastic Calculus and Applications

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Author(s): R. Bauerschmidt, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2018

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; stochastic processes

Introduction
The Lebesgue–Stieltjes integral
Semi-martingales
Finite variation processes
Local martingale
Square integrable martingales
Quadratic variation
Covariation
Semi-martingale
The stochastic integral
Simple processes
Ito isometry
Extension to local martingales
Extension to semi-martingales
Ito formula
The Lévy characterization
Girsanov's theorem
Stochastic differential equations
Existence and uniqueness of solutions
Examples of stochastic differential equations
Representations of solutions to PDEs
Index