In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin complexity in the context of Brownian motion and specifically to phenomena emerging from the random geometric patterns generated by a Brownian motion.

A Hilbert-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space. Since the integrator is not a semimartingale for the fractional Brownian motions considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach to integration has an analogue ...

Take two independent one-dimensional brownian motions (Bt; t 2 0; 1]) and (t; t 2 0; 1]) with B0 = 0 and 0 = 0 (can be seen as running backwards in time). Deene (t; t 2 0; 1]) as being the function that is obtained by reeecting B on. Then is still a Brownian motion. Similar and more general results (with families of coalescing Brownian motions) are also derived. They enable to give a precise de...

We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov Process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decompositi...

Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton–Watson forests with i.i.d. exponential branch lengths. We give e...

Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational...

The question of the equivalence in law of Gaussian processes has been widely studied in the sixties-seventies.(5,6,9,14) Recently, the problem has been reopened by several authors, due to the intensive study of the fractional Brownian and of stochastic calculus with respect to this process. Precisely, the Wiener integral representation of the fractional Brownian motion with respect to the Brown...

It is shown that the trapping of finite-sized spherical Brownian particles of radius /3R in a system of interpenetrable spherical traps of radius R is isomorphic to the trapping of “point” Brownian particles (p = 0) in a particular system of interpenetrable spherical traps of radius ( 1 + p> R. This isomorphism in conjunction with previous trapping-rate data for fl= 0 is employed to compute the...