On Brownian motion in a homogeneous Riemannian space

Hitting probabilities for Brownian motion on Riemannian manifolds

Brownian Motion in Minkowski Space

We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem. The first is to define a sequence of stopping times associated with the Brownian “kicks” or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, the Central Limit Theorem (CLT) leads to temperature d...

Brownian Motion close to Submanifolds of Riemannian Manifolds

We consider two different ways to force Brownian motion to be close to a submanifold of a riemannian manifold. We investigate their relationship and consider an application to the quantum mechanics of thin layers.

Brownian Motion in a Brownian Crack

Let D be the Wiener sausage of width ε around two-sided Brownian motion. The components of 2-dimensional reflected Brownian motion in D converge to 1-dimensional Brownian motion and iterated Brownian motion, resp., as ε goes to 0.

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory