Girsanov's Theorem: Numerical Simulation of SDEs

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

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

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

Explores martingale convergence, discussing the conditions for convergence and variance in martingales.

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.

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

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

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

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

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