Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging...

This paper establishes stochastic equicontinuity for classes of mixingales. Attention is restricted to Lipschitz-continuous parametric functions. Unlike some other empirical process theory for dependent data, our results do not require bounded functions, stationary processes, or restrictive...

We present general conditions for the weak convergence of a discrete-time additive scheme to a stochastic process with memory in the space D [ 0,T ]. Then we investigate the convergence of the related multiplicative scheme to a process that can be interpreted as an asset price with memory. As an...

In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the...

The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form integral_{0}^{1}WdW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the...

Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The...