Stochastic Calculus: Integrals and Processes

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Page 3 of 4

Sub- and Supermartingales: Theory and Applications

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

Martingales and Brownian Motion

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

Convergence of Adaptive Langevin using hypocoercivity

Covers the convergence of Adaptive Langevin dynamics using hypocoercive techniques and explores the Central Limit Theorem.

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

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.

Langevin dynamics: Path Integral Methods

Covers Langevin dynamics, Fokker-Planck equation, solving the Langevin equation, and efficiency of Langevin sampling in molecular dynamics.

Turbulent State Symmetries

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

Brownian Motion: From Molecules to Cells

Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.

Linear Response and Complex Diffusivity

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

Hausdorff Dimension and Brownian Motion

Explores Hausdorff dimension and its application to Brownian motion sets, emphasizing the importance of understanding set dimensions in stochastic processes.