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Stochastic Calculus and Applications

✍ Scribed by R. Bauerschmidt, ed. Dexter Chua

Publisher
University of Cambridge
Year
2018
Tongue
English
Leaves
51
Series
Cambridge Mathematical Tripos Part III Lecture Notes
Category
Library
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✦ Table of Contents

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 LΓ©vy characterization
Girsanov's theorem
Stochastic differential equations
Existence and uniqueness of solutions
Examples of stochastic differential equations
Representations of solutions to PDEs
Index

✦ Subjects

maths; mathematics; math; advanced; college; university; higher; further; pure; applied; stochastic processes

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