Stochastic Integration: First Steps

Related lectures (31)

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Covers the concept of joint quadratic processes and their properties.

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.

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

Explores martingale convergence, discussing the conditions for convergence and variance in martingales.

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

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

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

Explains the martingale convergence theorem and its applications in probability theory.

Covers semimartingales, Ito's lemma, and polynomial demonstrations, emphasizing the management of second-order terms and induction reasoning.

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.