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The pointwise limit S of a sequence of Stieltjes transforms (S n) of real Borel probability measures (P n) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) → −1 as y → ∞, in which case P n converges to P in distribution. Applications are given to several problems in mathematical physics. probability measures. Lévy's classical… (More)

- David Gllat, T P Hill
- 2006

Dedicated to Lester Dubins on his seventieth birthday. A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending… (More)

- T P Hill
- 2008

If asked whether certain digits in numbers collected randomly from, for example, the front pages of newspapers or from stock-market prices should occur more often than others, most people would think not. Nonetheless, in 1881, the astronomer and mathematician Simon Newcomb published a two-page article in the American Journal of Mathematics reporting an… (More)

- J Elton, T P Hill
- 2006

Starting with a Borel probability measure P on X (where X is a separable Banach space or a compact metrizable convex subset of a locally convex topological vector space), the class Y(P), called the fusions of P, consists of all Borel probability measures on X which can be obtained from P by fusing parts of the mass of P, that is, by collapsing parts of the… (More)

1. INTRODUCTION. In scientific calculations using digital computers and f1oating-point arithmetic, roundoff errors are inevitable, even with the most elementary of functions. For example, a very simple, hypothetical computer with only one decimal point precision, equipped with the IEEE Stand~d "Unbiase5!" Roundin& approximates the function f(x) = x 2 with a… (More)

- P Tremblin, V Minier, N Schneider, E Audit, T Hill, P Didelon +39 others
- 2016

Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. ABSTRACT Context. Herschel far-infrared imaging observations have revealed the density structure of the interface… (More)

- J Elton, T P Hill
- 2010

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case Žpurely. atomic measures with a finite number of atoms , and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on… (More)

Conditions are given for a C k map T to be a Newton map, that is, the map associated with a differentiable real-valued function via Newton's method. For finitely differentiable maps and functions, these conditions are only necessary, but in the smooth case, i.e. for k = ∞ , they are also sufficient. The characterisation rests upon the structure of the fixed… (More)

A sequence of real numbers (x n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x n), are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with * probability transition matrix P and limiting matrix P is Benford if every com n n+1 − P n) ponent of… (More)

- T P Hill, D P Kennedy
- 2006

A universal bound for the maximal expected reward is obtained for stopping a sequence of independent random variables where the reward is a nonincreasing function of the rank of the variable selected. This bound is shown to be sharp in three classical cases: (i) when maximizing the probability of choosing one of the k best; (ii) when minimizing the expected… (More)