Deaconu, Madalina Gradinaru, Mihai Roche, Jean Rodolphe

We study the heat diffusion in a domain with an obstacle inside. More precisely, we are interested in the quantity of heat in so far as a function of the position of the heat source at time 0. This quantity is also equal to the expectation of the sojourn time of the Brownian motion, reflected on the boundary of a small disk contained in the unit di...

Abraham, Romain Delmas, Jean-François
Published in
Probability Theory and Related Fields

We consider a Brownian snake (Ws,s≥0) with underlying process a reflected Brownian motion in a bounded domain D. We construct a continuous additive functional (Ls,s≥0) of the Brownian snake which counts the time spent by the end points Ŵs of the Brownian snake paths on ∂D. The random measure Z=∫δŴsdLs is supported by ∂D. Then we represent the solut...

Michalak, A. M. Kitanidis, P. K.
Published in
Stochastic Environmental Research and Risk Assessment

The objective of this work is to extend kriging, a geostatistical interpolation method, to honor parameter nonnegativity. The new method uses a prior probability distribution based on reflected Brownian motion that enforces this constraint. The work presented in this paper focuses on interpolation problems where the unknown is a function of a singl...

Hu, Qin Wang, Yongjin Yang, Xuewei
Published in
Computational Economics

Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis revea...

Demni, Nizar Lépingle, Dominique

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The...

Lange, Rutger-Jan

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, "Potential theory, path integrals and the Laplacian of the indicator", finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the...

Batakis, Athanasios Nguen, Hung

We show that the dimension of the exit distribution of planar partially reflected Brownian motion can be arbitrarily close to 2.

Lagnoux, Agnès Mercier, Sabine Vallois, Pierre

Probability that the maximum of the reflected Brownian motion over a finite interval [0, t] is achieved by its last zero before t Abstract We calculate the probability pc that the maximum of a reflected Brownian motion U is achieved on a complete excursion, i.e. pc := P U (t) = U * (t) where U (t) (respectively U * (t)) is the maximum of the proces...

Arnaudon, Marc Li, Xue-Mei

We construct a family of SDEs whose solutions select a reflected Brownian flow as well as a stochastic damped transport process (W_t). The latter gives a representation for the solutions to the heat equation for differential 1-forms with the absolute boundary conditions; it evolves pathwise by the Ricci curvature in the interior, by the shape opera...

Hanks, Ephraim M. Johnson, Devin S. Hooten, Mevin B.
Published in
Journal of Agricultural, Biological and Environmental Statistics

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modelin...