This paper gives a probabilistic interpretation of a class of nite diierence schemes often referred to as the-method. In particular, the present paper shows that for some parameter values the-method can been seen as a binomial tree with a random time.

Acknowledgements I wish to thank my dissertation advisor, Professor James S. Dyer for his insights and guidance. I would also like to recognize the other members of my dissertation Their comments and service were greatly appreciated. Dr. Luiz Brandao also provided many useful insights, and Dr. Jim Smith and Dr. John Butler were very helpful with computational matters. I would like to thank my p...

Accurate description of spatial distribution of species is essential for correctly modeling macroecological patterns and thus to infer mechanisms of species coexistence. The Poisson and negative binomial distribution (NBD) are most widely used to respectively model random and aggregated distributions of species in infinitely large areas. As a finite version of the Poisson distribution, the bino...

In this paper we summarise the experiences we obtained during past years in accelerating financial code through parallelisation and source-level optimisation. We have been focusing on developing optimised parallel programs to speedup financial computations where either binomial tree method or Monte Carlo simulation was applicable. The parallelisation was through explicit POSIX multi-threading o...

In 9] Knuth shows how to derive the convolution formulas of Ha-gen, Rothe and Abel from Vandermonde's convolution or binomial theorem for integer exponents. In the present paper, we shall rst present a short and elementary proof of the multi-extension of the above con-volution formulas, due to Raney and Mohanty. In the second part we shall present a multi-version of Knuth's approach to convolut...

Multi-band Wide – Band Code Division Multiple Access (W–CDMA) systems are considered to be among the best alternatives for Universal Mobile Telecommunications System (UMTS). To evaluate the performance of multi-band W–CDMA systems many parameters have to be taken into account. In this paper we present a method to evaluate the state space of multi-band overlaid W–CDMA system, and we present a ve...

It is demonstrated that in a two-stage scenario with elementary Poissonian emitters of particles (colour strings) arbitrarily distributed in their number and average multiplicities, the forward-backward correlations are completely determined by the final distribution of forward particles. The observed linear form of the correlations then necessarily requires this distribution to have a negative...