Delocalized Chern character for stringy orbifold K-theory

In this paper, we define a stringy product on K^*_{orb}(\XX) \otimes \C , the orbifold K-theory of any almost complex presentable orbifold \XX. We establish that under this stringy product, the de-locaized Chern character ch_{deloc} : K^*_{orb}(\XX) \otimes \C \longrightarrow H^*_{CR}(\XX), after a canonical modification, is a ring isomorphism. Here H^*_{CR}(\XX) is the Chen-Ruan cohomology of \XX. The proof relies on an intrinsic description of the obstruction bundles in the construction of Chen-Ruan product. As an application, we investigate this stringy product on the equivariant K-theory $K^*_G(G)$ of a finite group $G$ with the conjugation action. It turns out that the stringy product is different from the Pontryajin product (the latter is also called the fusion product in string theory).Comment: 34 pages. Final version to appear in Trans. of AMS. Improve the expositions and Change of the title thanks the referee

Nonstationary Discrete Choice

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n^{3/4} and n^{1/4}) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.Brownian motion, Brownian local time, Discrete choice model, Dual convergence rates, Extended arc sine laws, Integrated time series, Maximum likelihood estimation, Threshold parameters