Lecture

Stochastic Integration: First Steps

Related lectures (31)

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

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Stochastic Calculus: Integrals and Processes

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

Stochastic Integral: Isometry Continuity

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Sub- and Supermartingales: Theory and Applications

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

Martingales and Stochastic Integration

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Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Girsanov's Theorem: Numerical Simulation of SDEs

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Doob's Decomposition Theorem

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Joint Quadratic Processes

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Doob's Martingale

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Stochastic Calculus: Interest Rate Models

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

Martingale Convergence

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

Linear Response and Complex Diffusivity

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

Girsanov: Martingales and Brownian Motion

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Martingales and Brownian Motion Construction

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Martingale Convergence Theorem

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