共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper presents two main results: first, a Liapunov type criterion for the existence of a stationary probability distribution for a jump Markov process; second, a Liapunov type criterion for existence and tightness of stationary probability distributions for a sequence of jump Markov processes. If the corresponding semigroups TN(t) converge, under suitable hypotheses on the limit semigroup, this last result yields the weak convergence of the sequence of stationary processes (TN(t), πN) to the stationary limit one. 相似文献
2.
Dariya V. Safonova Maria V. Demina Nikolai A. Kudryashov 《Regular and Chaotic Dynamics》2018,23(5):569-579
In this paper we study the problem of constructing and classifying stationary equilibria of point vortices on a cylindrical surface. Introducing polynomials with roots at vortex positions, we derive an ordinary differential equation satisfied by the polynomials. We prove that this equation can be used to find any stationary configuration. The multivortex systems containing point vortices with circulation Γ1 and Γ2 (Γ2 = ?μΓ1) are considered in detail. All stationary configurations with the number of point vortices less than five are constructed. Several theorems on existence of polynomial solutions of the ordinary differential equation under consideration are proved. The values of the parameters of the mathematical model for which there exists an infinite number of nonequivalent vortex configurations on a cylindrical surface are found. New point vortex configurations are obtained. 相似文献
3.
Ildefonso Castro Francisco Torralbo Francisco Urbano 《Mathematische Zeitschrift》2012,271(1-2):257-270
Hamiltonian stationary Lagrangian spheres in K?hler-Einstein surfaces are minimal. We prove that in the family of non-Einstein K?hler surfaces given by the product Σ1?×?Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example, defined when the surfaces Σ1 and Σ2 are spheres, is unstable. 相似文献
4.
Leonenko Nikolai N. Sakhno Ludmila M. 《Statistical Inference for Stochastic Processes》2001,4(1):17-40
The limiting distributions are obtained for the Kaplan–Meier estimator of unknown distribution function of stationary time series of the form G(X
j), where X
j is stationary Gaussian process with long-range dependence and G(·) is non-random function. 相似文献
5.
Wenzhi Sun 《Archive for Mathematical Logic》1993,32(6):429-442
Summary This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly
1
1
-indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a
1
1
-indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent of that of a stationary cardinal. As applications, we will show thatV=L implies
1
holds if is
1
1
-indescribable and so forth. 相似文献
6.
Thierry de la Rue 《Bulletin of the Brazilian Mathematical Society》2006,37(4):503-521
V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process (ξi )i2ℤ, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold
mixing problem, the socalled 3-dot system, but in the context of stationary random fields indexed by ℤ2.
In this work, we first present an attempt to adapt Ledrappier's construction to the onedimensional case, which finally leads
to a stationary process which is 2-fold but not 3-fold mixing conditionally to the σ-algebra generated by some factor process. Then, using arguments coming from the theory of joinings, we will give some strong obstacles proving that Ledrappier's counterexample
can not be fully adapted to one-dimensional stationary processes. 相似文献
7.
Yu Miao 《Acta Appl Math》2009,106(2):177-184
Let X
k
=∑
i=−∞∞
a
i
ξ
k−i
,k≥1, be the moving average processes, where (ξ
i
)
i∈ℤ is a sequence of real stationary random variables. Under the assumptions that the large deviation principle (LDP) for real
stationary sequence holds, LDP for the moving average processes of real stationary sequence is established.
相似文献
8.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):249-264
Suppose Tukey's 3R (“running median”) smoothing algorithm is applied to a strictly stationary sequence X: = (Xk) of random variables, thereby creating a new stationary sequence X? If X satisfies the strong (Rosenblatt) mixing condition, then so does .X? If X is an i.i.d. sequence with each X(k:) uniformly distributed on the interval [0,1], then X? fails to be (mixing. Thus two questions of C. Mallows are answered. 相似文献
9.
Michel Sermange 《Applied Mathematics and Optimization》1986,14(1):131-153
The aim of this paper is to solve several mathematical and numerical questions related to the simulation of stationary and nonstationary premixed flat flames. Most of the results are obtained in the general context of complex chemical and diffusion mechanisms. The main mathematical results concern: (i) thea priori positivity of the mass fractions, and (ii) the sensitivity of the flame speed to the computational domain. The numerical method proposed for solving the stationary problem is a new combination of the pseudo-nonstationary approach, the Newton iterations, and the adaptive gridding. The computation of H2-O2-N2 flames with various initial concentrations (including the chemical extinction zone) shows the efficiency of this method. 相似文献
10.
Paweł J. Szabłowski 《随机分析与应用》2017,35(5):852-872
We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say m is a polynomial of degree at most m. We show that then under some additional, natural technical assumption there exists a family of orthogonal polynomial martingales. More precisely we show that such a family of processes is completely characterized by the sequence {(αn, pn)}n ? 0 where α′ns are some positive reals while p′ns are some monic orthogonal polynomials. Bakry and Mazet (Séminaire de Probabilit?s, vol. 37, 2003) showed that under some additional mild technical conditions each such sequence generates some stationary Markov process with polynomial regression.We single out two important subclasses of the considered class of Markov processes. The class of harnesses that we characterize completely. The second one constitutes of the processes that have independent regression property and are stationary. Processes with independent regression property so to say generalize ordinary Ornstein–Uhlenbeck (OU) processes or can also be understood as time scale transformations of Lévy processes. We list several properties of these processes. In particular we show that if these process are time scale transforms of Lévy processes then they are not stationary unless we deal with classical OU process. Conversely, time scale transformations of stationary processes with independent regression property are not Lévy unless we deal with classical OU process. 相似文献
11.
For the case of solidification of a bottom cooled binary alloy, the magnetohydrodynamic stationary and oscillatory convective stability in the mushy layer is investigated analytically using normal mode linear stability analysis. In the limit of large Stefan number (St), a near–eutectic approximation with large far field temperature is considered in the present research. To ascertain the instability in the mushy layer, the strength of the superimposed magnetic field is so chosen that it corresponds to a given mush Hartmann number (Ham) of the problem. The results are presented for various values of mush Hartmann numbers in the range, 0 ≤ Ham ≤ 50. The critical Rayleigh number for stationary convection shows a linear relationship with increasing Ham. The magnetohydrodynamic effect imparts a stabilizing influence during stationary convection. In comparison to that of the stationary convective mode, the oscillatory mode appears to be critically susceptible at higher values of β (β = St/℘2 ϒ2, ℘ is the compositional ratio, ϒ = 1 + St/℘), and vice versa for lower β values. Analogous to the behavior for stationary convection, the magnetic field also offers a stabilizing effect in oscillatory convection and thus influences global stability of the mushy layer. Increasing magnetic strength shows reduction in the wavenumber and in the number of rolls formed in the mushy layer. 相似文献
12.
Kenjiro Maginu 《Journal of Mathematical Analysis and Applications》1978,63(1):224-243
We consider a parabolic partial differential equation ut = uxx + f(u) on a compact interval of spatial variable x with Dirichlet boundary conditions. The stability of stationary solutions of this system is studied by the use of Liapunov's second method. We obtain necessary and sufficient conditions for the stability, asymptotic stability, neutral stability, instability, and conditional stability. These conditions are closely connected with the conditions for the existence of the stationary solutions. 相似文献
13.
《Statistics & probability letters》1987,5(2):143-147
We consider the asymptotic normality of the random variable Z(λ) = Σcj(λ)ζjasλ → ∞ where {ζj} is a strictly stationary strongly mixing sequence. 相似文献
14.
A nonlinear stability analysis of the stationary rotation of a system of five identical point vortices lying uniformly on a circle of radius R 0 outside a circular domain of radius R is performed. The problem is reduced to the problem of stability of an equilibrium position of a Hamiltonian system with a cyclic variable. The stability of stationary motion is interpreted as Routh stability. Conditions for stability, formal stability and instability are obtained depending on the values of the parameter q = R 2/R 0 2 . 相似文献
15.
Zhihao Ge Minfu Feng Yinnian He 《Journal of Mathematical Analysis and Applications》2009,354(2):708-815
In the paper, a stabilized multiscale finite element method for the stationary incompressible Navier-Stokes equations is considered. The method is a Petrov-Galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space. The stability of the P1-P0 triangular element (or the Q1-P0 quadrilateral element) is established. And the optimal error estimates of the stabilized multiscale finite element method for the stationary Navier-Stokes equations are obtained. 相似文献
16.
V. F. Butuzov 《Computational Mathematics and Mathematical Physics》2006,46(3):413-424
A stationary solution to the singularly perturbed parabolic equation ?u t + ε2 u xx ? f(u, x) = 0 with Neumann boundary conditions is considered. The limit of the solution as ε → 0 is a nonsmooth solution to the reduced equation f(u, x) = 0 that is composed of two intersecting roots of this equation. It is proved that the stationary solution is asymptotically stable, and its global domain of attraction is found. 相似文献
17.
Salehi and Scheidt [6] have derived several Wold-Cramér concordance theorems for q-variate stationary processes over discrete groups. In this paper we characterize the concordance of the Wold decomposition with respect to families arising in the interpolation problem and the Cramér decomposition for non-full-rank q-variate stationary processes over certain nondiscrete locally compact Abelian (LCA) groups. Moreover, we give an answer to a question of Salehi and Scheidt [6, p. 319] on a characterization of the Wold-Cramér concordance with respect to J0. As corollary we then deduce a characterization of J0-regularity. 相似文献
18.
The paper of Dong [Dong, J. Classical solutions to one-dimensional stationary quantum Navier–Stokes equations, J. Math Pure Appl. 2011] which proved the existence of classical solutions to one-dimensional steady quantum Navier–Stokes equations, when the nonzero boundary value u 0 satisfies some conditions. In this paper, we obtain a different version of existence theorem without restriction to u 0. As a byproduct, we get the existence result of classical solutions to the stationary quantum Navier–Stokes equations. 相似文献
19.
Richard C Bradley 《Stochastic Processes and their Applications》1983,14(1):67-77
We first give an extension of a theorem of Volkonskii and Rozanov characterizing the strictly stationary random sequences satisfying ‘absolute regularity’. Then a strictly stationary sequence {Xk, k = …, ?1, 0, 1,…} is constructed which is a 0?1 instantaneous function of an aperiodic Markov chain with countable irreducible state space, such that n?2 var (X1 + ? + Xn) approaches 0 arbitrarily slowly as n → ∞ and (X1 + ? + Xn) is partially attracted to every infinitely divisible law. 相似文献
20.
The Increment Ratio (IR) statistic (see (1.1) below) was introduced in Surgailis et al. [16]. The IR statistic can be used for testing nonparametric hypotheses for d-integrated (−1/2 < d < 5/4) behavior of time series, including short memory (d = 0), (stationary) long-memory (0 < d < 1/2), and unit roots (d = 1). For stationary/stationary increment Gaussian observations, in [16], a rate of decay of the bias of the IR statistic
and a central limit theorem are obtained. In this paper, we study the asymptotic distribution of the IR statistic under the
model X
t = X
t0 + g
N(t) (t = 1, …, N), where X
t0 is a stationary/stationary increment Gaussian process as in [16], and g
N(t) is a slowly varying deterministic trend. In particular, we obtain sufficient conditions on X
t0 and g
N(t) under which the IR test has the same asymptotic confidence intervals as in the absence of the trend. We also discuss the
asymptotic distribution of the IR statistic under change-points in mean and scale parameters.
Partially supported by the bilateral France-Lithuania scientific project Gilibert and Lithuanian State Science and Studies
Foundation, grant No. T-25/08. 相似文献