Stewart N. Ethier

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The Wright--Fisher model and its approximating diffusion model are compared in terms of the expected value of a smooth but arbitrary function of nth-generation gene frequency. In the absence of selection, this expectation is shown to differ in the two models by at most a linear combination (with coefficients depending only on the derivatives of the smooth(More)
Petrov constructed a diffusion process in the compact Kingman simplex whose unique stationary distribution is the two-parameter Poisson–Dirichlet distribution of Pitman and Yor. We show that the subset of the simplex comprising vectors whose coordinates sum to 1 is the natural state space for the process. In fact, the complementary set acts like an entrance(More)
Consider a wager that is more complicated than simply winning or losing the amount of the bet. For example, a pass line bet with double odds is such a wager, as is a bet on video poker using a specified drawing strategy. We are concerned with the probability that, in an independent sequence of identical wagers of this type, the gambler loses L or more(More)
That there exist two losing games that can be combined, either by random mixture or by nonran-dom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for the Parrondo player's sequence of profits, both in a one-parameter family of capital-dependent games and in a(More)
There are many situations in which grain distributions resulting from in situ hybridization of radioactively labeled probes to unique genes should be subjected to a statistical analysis. However, the problems posed by analysis of in situ hybridization data are not straightforward, and no completely satisfying method is currently available. We have developed(More)
A formula for the number of toroidal m × n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m × n binary arrays, allowing rotation and/or reflection of the rows and/or the columns.
The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here we(More)