Proofs of the Nonstationary Interpolation Theorems by Reduction to the Stationary Case

1998 ◽  
pp. 393-422
Author(s):  
C. Foias ◽  
A. E. Frazho ◽  
I. Gohberg ◽  
M. A. Kaashoek
Keyword(s):  
Stationary Case

An Inventory With Constant Demand and Poisson Restocking

1987 ◽  
Vol 1 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Laurence A. Baxter ◽  
Eui Yong Lee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Distribution Function ◽  
Poisson Process ◽  
Stationary Case ◽  
Stieltjes Transform ◽  
Partial Differential

An inventory whose stock decreases linearly with time is considered. The inventory may be replenished at the instants at which a deliveryman arrives provided that the level of the inventory does not exceed a certain threshold; deliveries are made according to a Poisson process. A partial differential equation for the distribution function of the level of the inventory is solved to yield a formula for the corresponding Laplace–Stieltjes transform. The evaluation of the transform is discussed and explicit results are obtained for the stationary case.

Force de répulsion entre un courant sinusoïdal linéique et une bande conductrice mince : application aux problèmes de lévitation

1994 ◽  
Vol 72 (9-10) ◽  
pp. 633-638
Author(s):  
M. T. Attaf ◽  
D. Allab
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Electromagnetic Interaction ◽  
Practical Interest ◽  
Stationary Case ◽  
Electromagnetic Field Distribution ◽  
Conducting Plate ◽  
Conducting Materials ◽  
Sinusoidal Current ◽  
Repulsive Forces

In a previous work, the authors presented a semianalytical treatment of the electromagnetic field distribution in the case of a straight conductor carrying a sinusoidal current parallel to a thin conducting plate. The result of this investigation is extended here to the evaluation of the repulsive forces accompanying this type of electromagnetic interaction. The variation of such forces with geometric parameters is studied in the presence of a single conductor, and in the case of several conductors laying in a plane parallel to the surface of the material submitted to the induction phenomenon. The problem of lévitation in steady-state conditions is examined, in the light of this arrangement, for various conducting materials. Graphs illustrate the results obtained and make evident their practical interest particularly in the stationary case of magnetically levitated vehicles.

Reflection of Shock Waves–1 Pseudo-Stationary Case

1956 ◽  
Vol 11 (5) ◽  
pp. 584-592 ◽  
Author(s):  
Ryuma Kawamura ◽  
Haruo Saito
Keyword(s):  
Shock Waves ◽  
Stationary Case

A model for a system subject to random shocks

1993 ◽  
Vol 30 (4) ◽  
pp. 979-984 ◽  
Author(s):  
Eui Yong Lee ◽  
Jiyeon Lee
Keyword(s):  
Distribution Function ◽  
Characteristic Function ◽  
Stochastic Model ◽  
Poisson Process ◽  
The State ◽  
Stationary Case ◽  
Random Shocks ◽  
Random Amount ◽  
Explicit Expressions

A Markovian stochastic model for a system subject to random shocks is introduced. It is assumed that the shock arriving according to a Poisson process decreases the state of the system by a random amount. It is further assumed that the system is repaired by a repairman arriving according to another Poisson process if the state when he arrives is below a threshold α. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t), if . The stationary case is also discussed.

The stochastic equation Yt+1 = AtYt + Bt with non-stationary coefficients

2001 ◽  
Vol 38 (1) ◽  
pp. 80-94 ◽  
Author(s):  
Ulrich Horst
Keyword(s):  
Global Convergence ◽  
Random Environment ◽  
Linear Relation ◽  
Stochastic Equation ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Convergence Result ◽  
Stationary Case ◽  
Finite Dimensional ◽  
Long Run

In this paper, we consider the stochastic sequence {Yt}t∊ℕ defined recursively by the linear relation Yt+1 = AtYt + Bt in a random environment which is described by the non-stationary process {(At, Bt)}t∊ℕ. We formulate sufficient conditions on the environment which ensure that the finite-dimensional distributions of {Yt}t∊ℕ converge weakly to the finite-dimensional distributions of a unique stationary process. If the driving sequence {(At, Bt)}t∊ℕ becomes stationary in the long run, then we can establish a global convergence result. This extends results of Brandt (1986) and Borovkov (1998) from the stationary to the non-stationary case.

scholarly journals ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL

2018 ◽  
Vol 35 (1) ◽  
pp. 198-231 ◽  
Author(s):  
Weilin Xiao ◽  
Jun Yu
Keyword(s):  
Strong Consistency ◽  
Asymptotic Theory ◽  
Least Squares Method ◽  
Estimation Method ◽  
Hurst Parameter ◽  
Stationary Case ◽  
Vasicek Model ◽  
Continuous Record ◽  
Recurrent Case ◽  
Two Parameters

This article develops an asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered.

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