Stochastic Calculus: Foundations and Applications

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Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Stochastic Calculus: Interest Rate Models

Provides an overview of stochastic calculus and its applications in interest rate models and financial modeling.

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.