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- S N Ethier, M F Norman
- Proceedings of the National Academy of Sciences…
- 1977

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)

(2000). A transition function expansion for a diffusion model with selection. Abstract Using duality, an expansion is found for the transition function of the reversible $K$-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time $t$ of… (More)

- S. N. Ethier
- 2014

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)

- S. N. Ethier, Jiyeon Lee
- 2009

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)

- Stewart N. Ethier, Jiyeon Lee
- ArXiv
- 2014

We study Toral's Parrondo games with N players and one-dimensional spatial dependence as modified by Xie et al. Specifically, we use computer graphics to sketch the Parrondo and anti-Parrondo regions for 3 ≤ N ≤ 9. Our work was motivated by a recent paper of Li et al., who applied a state space reduction method to this model, reducing the number of states… (More)

- Stewart N. Ethier, Carlos Gamez
- Games
- 2013

Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 × 2 88 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his… (More)

Fleming᎐Viot processes are probability-measure-valued diffusion processes that can be used as stochastic models in population genetics. Here we use duality methods to prove ergodic theorems for Fleming᎐Viot processes, including those with recombination. Coupling methods are also used to establish ergodicity of Fleming᎐Viot processes, first without and then… (More)

- W J Ewens, R C Griffiths, S N Ethier, S A Wilcox, J A Graves
- Genomics
- 1992

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)

- S. N. Ethier, Jiyeon Lee
- 2012

J o u r n a l o f P r o b a b i l i t y Electron. Abstract In Toral's games, at each turn one member of an ensemble of N ≥ 2 players is selected at random to play. He plays either game A , which involves transferring one unit of capital to a second randomly chosen player, or game B, which is an asymmet-ric game of chance whose rules depend on the player's… (More)

- S. N. Ethier
- 2013

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.