This paper studies a rental firm that offers reusable products to price- and quality-of-service-sensitive customers--Netflix or Blockbuster can be thought of as the canonical example. Customers' perception of quality is determined by their likelihood of obtaining the product or service...

In this paper, we propose a heteroskedastic model in discrete time which converges, when the sampling interval goes to zero, towards the complete model with stochastic volatility in continuous time described in Hobson and Rogers (1998). Then, we study its stationarity and moment properties. In...

In this paper, we have carried out a detailedstochastic analysis of the Ludwig-Jones–Holling modelpertaining to the occasional population burst ofthe spruce budworms in the coniferous forests of Canada.Our analysis explains the abrupt burst of the populationin the form of cusp catastrophe. A...

This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making...

The stationary distribution of a birth and death process may not be approximated by a diffusion. The general situation is illustrated on the "musical chairs" model by Binmore et al. (1995). <p>This model is shown to generate outcomes which are not captured by the concept of the ultralong run...</p>