On the Spectral Gap of Brownian Motion with Jump Boundary

Spectral Analysis of Brownian Motion with Jump Boundary

Consider a family of probability measures, indexed by ∂D, on a bounded open region D ⊂ Rd with a smooth boundary. For any starting point inside D, we run a standard d-dimensional Brownian motion in Rd until it first exits D, at which time it jumps to a point inside the domain D according to the jump measure at the exit point and starts a new Brownian motion. The same evolution is repeated indep...

On spectral simulation of fractional Brownian motion

This paper focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class of approximate methods that are based on the spectral properties of fBm’s stationary incremental...

Broadband boundary effects on Brownian motion.

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Browni...

On Brownian Motion in a Fluid with a Plane Boundary

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...