The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of theâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2005

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov modulated process based on an infinite Markov chain isâ€¦ (More)

Abstract This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infiniteâ€¦ (More)

Diophantine criteria occur naturally in the theory of partial differential equations through the notorious problem of small denominators. An extensive treatment of such problems in the theory of PDEsâ€¦ (More)

Two simple theorems are proved about the auto-correlation function (ACF) of weakly stationary time series which can only take two values. The first theorem shows how the ACF can be expressed in termsâ€¦ (More)

The metrical theory of Diophantine approximation for quate rnions is developed using recent results in the general theory. In particular, Quaternionic analogues of t he classical theorems ofâ€¦ (More)

The theory of diophantine approximation studies how well x = (x1, . . . , xn) âˆˆ R can be approximated by (p1/q1, . . . , pn/qn) âˆˆ Q of a given â€˜complexityâ€™, where this complexity is usually measuredâ€¦ (More)

Let C be two times continuously differentiable curve in R with at least one point at which the curvature is non-zero. For any i, j > 0 with i + j = 1, let Bad(i, j) denote the set of points (x, y) âˆˆâ€¦ (More)