Lectures related to Stratonovich integral

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Stochastic Calculus: Integrals and Processes

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

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

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

Stochastic Calculus: Brownian Motion

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

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

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.

Convergence of Adaptive Langevin using hypocoercivity

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

Stochastic Calculus: Foundations and Applications

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

Ito Lemma Variants

Explores the Ito Lemma and its variants, discussing localization and proof techniques.

Asset Pricing Theory: Dynamic Arbitrage Pricing

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

Integral Calculus: Techniques and Applications

Explores integral calculus techniques, areas under graphs, Darboux sums, and the fundamental theorem of calculus.

Derivative of Integral with Parameter Dependency

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

Linear Hatching Systems: Unique Solutions and Norm Introduction

Explores linear hatching systems, unique solutions, norms, and fixed points in linear systems.

Demonstration of Uniqueness Theorem

Presents a detailed proof of the uniqueness theorem for functions f and g.

Stochastic Calculus: Itô's Formula

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

Integral Calculus: Introduction and Summary

Provides an overview of integral calculus, including Darboux sums, closed box subdivisions, and integrability of continuous functions.

Martingales and Brownian Motion Construction

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

Path Integral Methods: Advanced Techniques

Explores advanced path integral methods in computational science, covering efficient sampling, colored noise, high-order integrals, and quantum thermostats.