Central Limit Theorems
Central limit theorems describe the behaviour of distributions of sums of random variables. We start with the classical result of distributions of sums of independent random variables converging to the Gaussian (bell-curve) distribution. We describe the most important cases of convergence to Gaussian distributions (sums of martingale differences) as well as convergence to other distributions.
KeywordsCentral limit theorems Convergence Edgeworth expansions Feller condition Laplace, P. S. Lindeberg condition Long-term variance Lyapunov condition Martingale differences Maximum likelihood Monte Carlo simulation
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