Motivated by questions related to a fragmentation process which has been studied by Aldous, Pitman, and Bertoin, we use the continuous-time ballot theorem to establish some results regarding the lengths of the excursions of Brownian motion and related processes. We show that the distribution of the lengths of the excursions below the maximum for Brownian motion conditioned to rst hit > 0 at tim...

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...

Motivated from Gaussian processes, we derive the intrinsic volumes of the infinite–dimensional Brownian motion body. The method is by discretization to a class of orthoschemes. Numerical support is offered for a conjecture of SangwineYager, and another conjecture is offered on the rate of decay of intrinsic volume sequences.

The following question is due to Marc Yor: Let B be a Brownian motion and St = t+Bt. Can we define an F-predictable process H such that the resulting stochastic integral (H ·S) is a Brownian motion (without drift) in its own filtration, i.e. an F(H·S)-Brownian motion? In this paper we show that by dropping the requirement of F-predictability of H we can give a positive answer to this question. ...

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...

in this paper the effect of using various models for conductivity and viscosity considering brownian motion of nanoparticles is investigated. this study is numerically conducted inside a cavity full of water-al2o3 nanofluid at the case of mixed convection heat transfer. the effect of some parameters such as the nanoparticle volume fraction, rayleigh, richardson and reynolds numbers has been exa...

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 ...

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...

This paper considers large sample approximations to the covariances of a nonstationary fractionally integrated processes with the stationary increments of another such process – possibly, itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analysed in a previous paper, and the construction derived from moving averag...