We first introduce a new variant of the tempered stable distribution, named the modified tempered stable(MTS) distribution and we use it to develop the GARCH option pricing model with MTS innovations. This model allows one to describe some stylized phenomena observed in financial markets such as volatility clustering, skewness, and heavy tails of the return distribution.

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one wi...

This paper documents the process and outcomes of a digital design project with the aim of translating music into architecture. Parametric software has been used to generate 48 virtual forms from the preludes and fugues of Book I of The Well-Tempered Clavier (BWV 846-869), by Johann Sebastian Bach. The paper discusses historical connections between architecture and music in the Western tradition...

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided and two-sided derivatives. An analysis of Riesz potential is done shows that it cannot be considered as a derivative.

We extend the ridgelet transform to the space of tempered Boehmians consistent with the ridgelet transform on the space of tempered distributions. We also prove that the extended ridgelet transform is continuous, linear, bijection and the extended adjoint ridgelet transform is also linear and continuous. AMS Mathematics Subject Classification (2010): 44A15, 44A35, 42C40

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation π such that O occurs in the wave front cycle of π. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.

In this paper we study the asymptotic dynamics for the nonautonomous stochastic strongly damped wave equation driven by additive noise defined on unbounded domains. First we introduce a continuous cocycle for the equation and then investigate the existence and uniqueness of tempered random attractors which pullback attract all tempered random sets.