Girsanov's Theorem: Numerical Simulation of SDEs

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Page 3 of 4

Explains the martingale convergence theorem and its applications in probability theory.

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

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Explores risk-neutral valuation for European derivatives, EMMs, trading strategies, and market securities in financial modeling.

Covers the concept of joint quadratic processes and their properties.

Covers the proof of the martingale convergence theorem and the convergence of the martingale sequence almost surely.

Explores the optional stopping theorem for martingales and stepping times, emphasizing its applications and implications.

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

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.