Concept

Stochastic calculus

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 Calculus: Brownian Motion

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

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Spatial Ergodicity for SPDEs

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

Stochastic Calculus: Interest Rate Models

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

Turbulent State Symmetries

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

Martingale-based Methods for Stochastic Systems

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

Stochastic Calculus: Foundations and Applications

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

Fourier Transform and Spectral Densities

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

Stochastic Differential Equations

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

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

Controlled Stochastic Processes

Explores controlled stochastic processes, dynamic programming, and the Machine Replacement Problem.

Asset Selling: Optimal Revenue Policy

Explores asset selling dynamics, optimal revenue policy, acceptance thresholds, and commodity price impact.

Martingales and Brownian Motion Construction

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

Stochastic Calculus: Lecture 1

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

Stochastic Calculus: Integrals and Processes

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

Linear Response and Complex Diffusivity

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

Derivative of Integral with Parameter Dependency

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

Martingales and Brownian Motion

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