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We consider a reflected Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter $H\in(0,1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\inft...
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 ...
I met Peter J. Bickel for the first time in 1981. He came to Jerusalem for a year; I had just started working on my Ph.D. studies.
Random walks with random indices and negative drift conditioned to stay positive。
First hitting times and positions of concentric spheres for testing the drift of a diffusion process。
Azema martingales with drift      Azema martingales  drift       2009/9/22
Pursuing the earlier work of Emery [I], Meyer [2], [3] and the author [4] it is shown that Akma martingales starting from a varying initial point on the line constitute an Evans-Hudson flow in the ...
In this paper, we study backward stochastic nonlinear Volterra integral equations. Under a local Lipschitz continuity condition on the drift, we prove the existence and uniqueness result. We also e...
In this paper, we investigate the consistency and asymptotic efficiency of an estimator of the drift matrix, $F$, of Ornstein-Uhlenbeck processes that are not necessarily stable. We consider all the c...
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form dU(t) = (AU(t) + f) dt + B dWH(t), governed by the generator A of...
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form dU(t) = (AU(t) + f) dt + B dWH(t),governed by the generator A of an asympto...
We study the dynamical properties of the Brownian diffusions having σ Id as diffusion coefficient matrix and b=∇U as drift vector. We characterize this class through the equality D+2=D-2, where ...
We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry gr...

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