Suppose a1, a2,... is a sequence of real numbers with an → ∞. If $\lim \sup(X_1 + \cdots + X_n)/a_n = \alpha$ a.s. for every sequence of independent nonnegative uniformly bounded random variables X1, ...

The present paper considers the stochastic difference equation Yn=AnYn-1+Bn with i.i.d. random pairs (An,Bn) and obtains conditions under which Yn converges in ...

A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3, . . . For example, stock prices are discrete random variables, ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

According to this post on the official V8 Javascript blog, the pseudo-random number generator (PRNG) that V8 Javascript uses in Math.random() is horribly flawed and getting replaced with something a ...

B.F. Skinner was a renowned American psychologist and behaviorist. He made great contributions to the fields of psychology and sociology and one of his most helpful theories was that of operant ...