8 citations · 8 across the 7 of their papers we have counts for
9 papers
Local time of Martin-Lof Brownian motion
Willem Fouche, Safari Mukeru
In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path w…
On the inverse problem of fractional Brownian motion and the inverse of infinite Toeplitz matrices
Safari, Mukeru, Mmboniseni P +1
The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matr…
Zeros of Gaussian power series, Hardy spaces and determinantal point processes
Safari Mukeru, Mmboniseni P. Mulaudzi
Given a sequence of standard i.i.d complex Gaussian random variables, Peres and Virág (in the paper ``Zeros of the i.i.d. Gaussian power series: a conformally invariant det…
Some applications of the Menshov-Rademacher theorem
Safari Mukeru
Given a sequence of real or complex random variables and a sequence of numbers , an interesting problem is to determine the conditions under which the series $\sum_{…
A generalisation of Pisier homogeneous Banach algebra
Safari Mukeru
In 1979 Pisier proved remarkably that a sequence of independent and identically distributed standard Gaussian random variables determines, via random Fourier series, a homogeneous…
Generalisation of Fractional-Cox-Ingersoll-Ross Process
Marc Mukendi Mpanda, Safari Mukeru, Mmboniseni Mulaudzi
In this paper, we define a generalised fractional Cox-Ingersoll-Ross process as a square of singular stochastic differential equation with respect to fractional Brownian motion wit…
On the convergence of series of dependent random variables
Safari Mukeru
Given a sequence of symmetrical random variables taking values in a Hilbert space, an interesting open problem is to determine the conditions under which the series $\sum_{…
Average number of real roots of random polynomials defined by the increments of fractional Brownian motion
Safari Mukeru
The study of random polynomials has a long and rich history. This paper studies random algebraic polynomials where the coefficient…
Fourier spectra of measures associated with algorithmically random Brownian motion
Willem Louw Fouché, Safari Mukeru, George Davie
In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion.…