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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...
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 ...
Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter $H \in (1/4,1/2)$
fractional Brownian motion stochastic non-Newtonian fluid
2011/7/19
In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst parameter $H \in (1/4,1/2)$...
Reconstruction of Fractional Brownian Motion Signals From Its Sparse Samples Based on Compressive Sampling
Compressive Sampling fractional Brownian motion interpolation financial time-series fractal
2011/6/21
This paper proposes a new fBm (fractional Brownian
motion) interpolation/reconstruction method from partially
known samples based on CS (Compressive Sampling). Since 1/f
property implies power law ...
Identification of the Multivariate Fractional Brownian Motion
Self similarity Multivariate process Long-range dependence Discrete variations Parametric estimation
2011/3/21
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p...
Identification of the Multivariate Fractional Brownian Motion
Self similarity Multivariate process Long-range dependence Discrete variations Parametric estimation
2011/3/23
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p...
Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus
discrete Wick calculus fractional Brownian motion weak convergence
2010/10/19
We approximate the solution of some linear systems of SDEs driven by a fractional Brownian motion $B^H$ with Hurst parameter $H\in(\frac{1}{2},1)$ in the Wick--It\^{o} sense, including a geometric fra...
On the almost sure convergence of the square variation of the Brownian motion
the almost sure convergence the square variation the Brownian motion
2009/9/24
On the almost sure convergence of the square variation of the Brownian motion。
Weak convergence to the Brownian motion of the partial sums of infima of independent random variables
Weak convergence the Brownian motion independent random variables
2009/9/23
Weak convergence to the Brownian motion of the partial sums of infima of independent random variables。