Stochastic Integration

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Related lectures (31)

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 Differential Equations

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

Stochastic Calculus: Interest Rate Models

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

Stochastic Calculus: Foundations and Applications

Explores the foundation of stochastic calculus, emphasizing deterministic and memoryless processes.

Turbulent State Symmetries

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

Fourier Transform and Spectral Densities

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

Stochastic Integration: First Steps

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

Martingales and Stochastic Integration

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

Asset Pricing Theory: Dynamic Arbitrage Pricing

Covers the first theorem of asset pricing, self-financing portfolios, replication, Kolmogorov equations, and pricing strategies.

Interest Rate Models: Introduction

Covers the fundamentals of interest rates and stochastic models in finance.

Martingale-based Methods for Stochastic Systems

Explores martingales in stochastic systems, focusing on formal analysis, termination analysis, and stability verification.

Spatial Ergodicity for SPDEs

Explores spatial ergodicity for SPDEs, covering basic formulations, initial data effects, and results on ergodicity and CLT.

Sub- and Supermartingales: Theory and Applications

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

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Linear Response and Complex Diffusivity

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

Fokker-Planck Equation: Derivations and Applications

Explores the derivation of the Fokker-Planck equation and its applications in stochastic differential equations.

Mean Field Theory: Stochastic Analysis and Applications

Explores classical mean field theory, local interactions, and examples like individual-based SIR models and raindrop formation.

Response Theory and Phase Transitions

Explores response theory, phase transitions, and fluctuations in weakly interacting systems, including stochastic particles and opinion formation models.

Optimal Distributed Control: Projected GD for Locally Optimal Controllers

Covers optimal distributed control using Gradient Descent to achieve locally optimal controllers in large-scale systems.

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