This article describes how nowadays, data is widely transmitted over the internet in the real time. Wherever the transmission or storage is required, security is needed. High speed processing hardware machine with reduced complexity are used for the security of the data, that are transmitted in...

The classic contingent-claims pricing model views the borrower’s right to default ona mortgage as a put option. By defaulting on a mortgage the borrower effectivelysells the property to the lender with the current value of the mortgage. The primarygoal of this dissertation is to develop a...

We prove computable versions of limsup events and Borel–Cantelli-like results for algorithmically random sequences using a coefficient from Kolmogorov complexity. In particular we show that under suitable conditions on events, limsup is layerwise decidable.

Integrands that depend on a large number of equally important variables are considered and conditions that make expedient quasi-Monte Carlo integrations are investigated for dimensions n≤300.

A “universal” fitting function has been recognized that makes use of the eigen-coordinates method (Physica A 285 (2000) 547) to accurately describe the distribution of ordered amplitudes within random sequences (taken from a diversity of sources). It is shown that sequences with a discrete...

Recently, Percus derived probabilities and distributions for parallel, i.i.d. random sequences of integers. This was accomplished by considering s given bit locations in each random variable (represented as a predetermined number of bits) in each sequence. These s bits were used to create a new...

Infinite sequences of random (nearly independent) binary digits can be generated having (almost certainly) a remarkable property. Observation of any nonzero fraction such as sequence makes it possible to calculate the values of all the unobserved digits.