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Multitype Branching Brownian Motion and Traveling Waves
Multitype branching Brownian motion Spine approach Ad- ditive martingale Traveling wave solution
2016/1/25
This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
Multitype Branching Brownian Motion and Traveling Waves
Multitype branching Brownian motion Spine approach Ad- ditive martingale Traveling wave solution
2016/1/20
This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
A classical model of Brownian motion consists of a heavy molecule
submerged into a gas of light atoms in a closed container. In this work
we study a 2D version of this model, where the molecule is a...
Homogenization driven by a fractional Brownian motion:the shear layer case
Homogenization driven fractional Brownian motion shear layer case
2015/7/14
We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when th...
Discretization Error in Simulation of One-dimensional Reflecting Brownian Motion
Discretization Error Simulation One-dimensional Reflecting Brownian Motion
2015/7/8
This paper is concerned with various aspects of the simulation of one-dimensional reflected (or regulated) Brownian motion. The main result shows that the discretization error associated with the Eule...
On the Maximum Workload of a Queue Fed by Fractional Brownian Motion
Long-range dependence queues fractional Brownian motion extreme values
2015/7/8
Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interva...
Conditional Limit Theorems for Regulated Fractional Brownian Motion
Queues fractional Brownian motion conditional limit laws large buffer asymptotic
2015/7/6
We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value b, we provide the limiting distribution for the am...
Fractional Brownian Motion with H<1/2 As a Limit of Scheduled Traffic
Fractional Brownian Motion Limit Scheduled Traffic
2015/7/6
This paper shows that fractional Brownian motion with H<12 can arise as a limit of a simple class of traffic processes that we call “scheduled traffic models”. To our knowledge, this paper provides th...
Measuring the Initial Transient: Reflected Brownian Motion
Measuring Initial Transient Reflected Brownian Motion
2015/7/6
We analyze the convergence to equilibrium of one-dimensional re flected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximatio...
The maximum likelihood drift estimator for mixed fractional Brownian motion
mixed fractional Brownian motion maximum likelihood estimator large sample asymptotic
2012/9/18
The paper is concerned with the maximum likelihood estimator (MLE) of the unknown drift parameterθ∈Rin the continuous-time regression model Xt =θt+Bt +BHt,t ∈[0, T] whereBt is the Brownian motion and ...
Derivative Formula, Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motion
Derivative formula integration by parts formula Harnack inequality stochastic differential equation fractional Brownian motion
2012/6/21
In the paper, the Bismut derivative formula is established for multidimensional SDEs driven by additive fractional noise ($1/2and moreover the Harnack inequality is given. Through a Lamperti t...
First Passage Times for a Tracer Particle in Single File Diffusion and Fractional Brownian Motion
First Passage Times Tracer Particle Single File Diffusion Fractional Brownian Motion Biological Physics
2012/5/29
We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles ...
Active Brownian motion of an asymmetric rigid particle
Active Brownian motion asymmetric rigid particle Biological Physics
2012/5/17
Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococc...
On the time inhomogeneous skew Brownian motion
Skew Brownian motion Local times Stochastic differential equation balayage formula Skorokhod problem
2012/4/23
This paper is devoted to the construction of a solution for the "Inhomogenous skew Brownian motion" equation, which first appeared in a seminal paper by Sophie Weinryb, and recently, studied by \'{E}t...
Dyson's Brownian Motion Model as a Special Case of Dunkl Processes and Dunkl's Intertwining Operators
Dyson's Brownian Motion Model Special Case Dunkl Processes Dunkl's Intertwining Operators
2012/2/27
Dyson's Brownian motion model is a one-parameter family of log-potential interacting particle systems in one dimension parametrized by an inverse temperature beta > 0. When beta = 1, 2 and 4, this mod...