Farzad Sabzikar

Post date: Aug 28, 2013 7:23:01 PM

1. Tempered fractional Brownian motion

2. Tempered fractional calculus

Abstract 1: Tempered fractional Brownian motion (TFBM) modifies the power law kernel in the moving

average representation of a fractional Brownian motion, adding an exponential tempering.

Tempered fractional Gaussian noise (TFGN), the increments of TFBM, form a stationary time

series that can exhibit semi-long range dependence. This paper develops the basic theory

of TFBM, including moving average and spectral representations, sample path properties,

and an application to modeling wind speed.

Abstract 2: Tempered fractional integral (TFI) is a bounded linear operator and keeps the spaces Lp(R) invariant. The stochastic integral of deterministic functions

with respect to tempered fractional Brownian motion (TFBM) will be investigated. As a consequence , the Mat.ern covariance function will be shown as a tempered fractional integral of white noise.