Translation and convolution associated with discrete wavelet transform are investigated using properties of Calderón-Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain p L-spaces.

The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the Lévy stable distributions, and more generally the probability distributions governed by generalized diffusion equations of fractional order in space and/or in time. In these cases the related stochast...

Schürmann's theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalge-bras. Quantum stochastic convolution cocycles on a C *-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic ...

Schürmann’s theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic dif...

We show how a technique from signal processing known as zero-delay convolution can be used to develop more efficient dynamic programming algorithms for a broad class of stochastic optimization problems. This class includes several variants of discrete stochastic shortest path, scheduling, and knapsack problems, all of which involve making a series of decisions over time that have stochastic con...