Convergence of Dependent Random Variables. Central Limit Theorems, Berry-Esseen Bounds, Martingale-like Sequences, C-sequences, Strong Laws

Self-organized criticality:bak (1996). Pioneers of fat tails:for wealth, pareto (1896), yule (1925,1944). less of a pioneer Zipf (1932, 1949). For linguistics, see Mandelbrot (1952). Pareto:see bouvier (1999). Endogenous vs. exogenous:sornette et al. (2004). SperberБЂ™s work: Sperber (1996a, 1996b, 1997). Regression: If you hear the phrase least square regression, you should be suspicious about the claims being made. As it assumes that your errors wash out rather rapidly, it underestimates the total possible error, and thus overestimates what knowledge one can derive from the data. The notion of central limit:very misunderstood: it takes a long time to reach the central limitБЂ”so as we do not live in the asymptote, weБЂ™ve got problems. All various random variables (as we started in the example of Chapter 16 with a +1 or БЂ“1, which is called a Bernouilli draw) under summation (we did sum up the wins of the 40 tosses) be: come Gaussian. Summation is key here, since we are considering the results of adding up the 40 steps, which is where the Gaussian, under the first and second central assumptions becomes what is called a БЂњdistribution.БЂ«(A distribution tells you how you are likely to have your outcomes spread out, or distributed.) However, they may get there at different speeds ...»