Casey Murphy has fanned his passion for finance through years of writing about active trading, technical analysis, market commentary, exchange-traded funds (ETFs), commodities, futures, options, and ...

Let $\{X_i\}$ be a sequence of independent, identically distributed nondegenerate random variables and $S_n = \sum^n_{i = 1}X_i$. We consider the question for various ...

Let {Sn, n ≥ 1} be a zero, mean square integrable martingale for which $\lim_{n\to\infty}ES_{n}^{2}<\infty$ so that Sn → S∞, a.s., say, by the martingale convergence theorem. The paper is principally ...

Logarithm of the ratio of the probability of obtaining a set of observations, assuming a specified degree of linkage, to the probability of obtaining the same set of observations with independent ...