Doob's Decomposition TheoremCovers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.
Martingale ConvergenceExplores martingale convergence, discussing the conditions for convergence and variance in martingales.
Turbulent State SymmetriesExplores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.
Doob's MartingaleCovers the concept of Doob's martingale and its properties, including integrability and convergence theorem.