Itô calculus

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Related lectures (31)

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Ito Lemma Variants

Explores the Ito Lemma and its variants, discussing localization and proof techniques.

Demonstration of Uniqueness Theorem

Presents a detailed proof of the uniqueness theorem for functions f and g.

Derivative of Integral with Parameter Dependency

Explores the derivative of an integral with parameter dependency and its continuity.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Girsanov: Martingales and Brownian Motion

Explores martingales, Brownian motion, and measure transformations in probability theory.

Variational Calculus: Quasicovexity

Explores quasicovexity in variational calculus, discussing necessary conditions and implications on functional optimization.

Martingales and Stochastic Integration

Covers martingales, stochastic integration, and localizing processes using stopping times.

Martingales and Brownian Motion Construction

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

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Integral Calculus: Introduction and Summary

Provides an overview of integral calculus, including Darboux sums, closed box subdivisions, and integrability of continuous functions.