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Related lectures (31)

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Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Stochastic Optimal Control: Martingale Theorem

Explores Stochastic Optimal Control, emphasizing Optimal Consumption and Investment, the Martingale Representation Theorem, and the Verification Theorem.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Advanced Analysis II: Riemann Integrability and Jordan Measure

Explores Riemann integrability and Jordan measure, discussing the conditions for a set to be negligible.

Turbulent State Symmetries

Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Stochastic Differential Equations

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

Integral Calculus of Functions in Several Variables

Covers the integration of functions in several variables, Darboux sums, and Fubini's theorem on a closed box.

Semimartingale: Joint Variation Process

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

Martingale Convergence Theorem: Proof and Stopping Time

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Stochastic Calculus: Lecture 1

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