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Fluctuation bounds for the asymmetric simple exclusion process
exclusion process particle current second class particle coupling moment bound fluctuations
2009/6/15
We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the order...
We determine the law of the convex minorant $(M_s, sin [0,1])$ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that t...
Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes
Wishart and Laguerre ensembles and processes eigenvalues as diffusions non-colliding squared Bessel processes
2009/5/4
Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the La...
Large Deviations and Quasi-Potential of a Fleming-Viot Process
Fleming-Viotprocess largedeviations quasi-potential
2009/4/29
The large deviation principle is established for the Fleming-Viot process with neutral mutation when the process starts from a point on the boundary. Since the diffusion coefficient is degenerate on t...
A recent theorem by M. Manstavicius (2004) provided a link between a certain function of transition probabilities of a strong Markov process and the boundedness of the p-variation of its trajectories....
A Resummed Branching Process Representation for a Class of Nonlinear ODEs
Branching processes Nonlinear dierential equations Resummation
2009/4/24
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
Chung, Diaconis, and Graham considered random processes of the form Xn+1=2Xn+bn (mod p) where X0=0, p is odd, and bn for n=0, 1, 2, ... are i.i.d. random variables on {-1,0,1}. If Pr(bn=-1)=Pr(bn=1)= ...
Yule process sample path asymptotics
Large deviations random trees branching process fluid limit Yule process
2009/4/22
This paper presents two results on sample paths for the Yule process: one fluid limit theorem and one sample path large deviation result. The main interest is to understand the way large deviation occ...
Filtering and parameter estimation for a jump stochastic process with discrete observations
Filtering parameter estimation discrete observations
2009/3/19
A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian settin...