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Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators i...
Consider an OrnsteinUhlenbeck process with reflection at the origin. Such a process arises as an approximating process both for queueing systems with reneging or state-dependent balking and for multi...
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...
We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour with heavy distribu...
Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\'{e}vy process (FLP). To explicitly solve general fractional stochastic ...
We consider a positive stationary generalized OrnsteinUhlenbeck process Vt = e−tZ t0es− ds + V0 for t  0,and the increments of the integrated generalized OrnsteinUhlenbeck process...
Sufficient conditions for equivalence of distributions in LZ(O,T , H) of two Ornstein-Uhlenbeck processes taking values in a Hilbert space H are given. The Girsanov theorem and some facts in the th...
We prove the existence of an Omstein-Uhlenbeck type process associated with the Evy Laplacian. Like the classical case, the law of the Levy Brownian motion at time 1 is an invariant probability of ...
Several concrete parametric classes of tempered stable distributions are discussed in terms of explicit calculations of their Rosihki measures. The hope is that they will provide a family of concre...
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...
We show that the multiplication operator associated to a fractional power of a Gamma random variable, with parameter q > 0, maps the convex cone of the 1-invariant functions for a self-similar semigro...
The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in R^2 and R^3. We assume that the flow is driven by an incompressible time-dependent random veloci...
The Laplace transform of the first exit time from a finite interval by a regular spectrally negative α-stable Ornstein-Uhlenbeck process is provided in terms of the Wright's generalized hypergeometric...
The Laplace transform of the first exit time from a finite interval by a regular spectrally negative α-stable Ornstein-Uhlenbeck process is provided in terms of the Wright's generalized hypergeometric...
We study a least squares estimator bT for the Ornstein-Uhlenbeck process, dXt = Xtdt+dBHt , driven by fractional Brownian motion BH with Hurst parameter H  12 . We prove the strong consistence o...

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