An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative ("mutant") strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases:...

We prove a difference equation analogue for the decay-of-mass result for the nonlinear parabolic equation ut = ?u + m |?u| when m < 0, and a new growth result when m > 0.

Let X1, ... , Xn be n random variables, with cumulative distribution functions F1, ... , Fn. Define [xi]i: = Fi(Xi) for all i, and let [xi](1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] [xi](n) be the order statistics of the ([xi]i)i. Let [alpha]1 [less-than-or-equals, slant]...

Our main purpose is to present a very surprising new characterization of the Shannon entropy of stationary ergodic processes. We will use two basic concepts: isomorphism of stationary processes and a notion of finite observability, and we will see how one is led, inevitably, to Shannon's...

The forecasting problem for a stationary and ergodic binary time series {Xn} is to estimate the probability that Xn+1 = 1 based on the observations Xi, 0 = i = n without prior knowledge of the distribution of the process {Xn}. It is known that this is not possible if one estimates at all values...

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1,…,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for...