Kolmogorov complexity and the geometry of Brownian motion

Kolmogorov Complexity and Strong Approximation of Brownian Motion

Brownian motion and scaled and interpolated simple random walk can be jointly embedded in a probability space in such a way that almost surely, the n-step walk is within a uniform distance O(n−1/2 log n) of the Brownian path, for all but finitely many positive integers n. Almost surely, this n-step walk will be incompressible in the sense of Kolmogorov complexity, and all Martin-Löf random path...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...

Fourier spectra of measures associated with algorithmically random Brownian motion

Abstract. 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. We show that, under some computability conditions on these sets, the Fourier transform of the associated measures have, relative to the Hausdorff dimensions of these sets, optimal asymptotic decay at infini...

CFD simulations on natural convection heat transfer of alumina-water nanofluid with Brownian motion effect in a 3-D enclosure

The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...