共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent
innovations. Let {X
t
} be a linear process defined by X
t
= Σ
k=0∞ψ
k
ɛ
t−k
, where {ψ
k
, k ≥ 0} is a sequence of real numbers and {ɛ
k
, k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that
{ɛ
k
, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting
distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption
of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency
estimator of the autoregressive parameter α when {ɛ
k
, k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ
0 = 1, ψ
k
= 0, k ≥ 1. 相似文献
2.
The problem of H_∞filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper.By applying an innovation analysis in Krein space,a necessary and sufficient condition for the existence of an H_∞filter is derived in two methods:One is the partial differential equation approach,the other is the reorganized innovation analysis approach.The former gives a solution to the proposed H_∞filtering problem in terms of the solution of a partial differential equation with boundary conditions.The later gives an analytical solution to the proposed H_∞filtering problem in terms of the solutions of Riccati and matrix differential equations. 相似文献
3.
In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆
p
u = f(x)u
−α + λg(x)u
β in R
N
; where N ≥ 3, 1 < p < N, λ > 0, 0 < α < 1, max(p, 2) < β + 1 < p* =
\fracNpN - p \frac{{{N_p}}}{{N - p}} . We prove that there exists a critical value ¤ such that the problem has at least two solutions if 0 < λ < Λ; at least one
solution if λ = Λ; and no solutions if λ > Λ. 相似文献
4.
This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence
analysis shows that the method yields the approximate solutions with optimal accuracy in (L
2(Ω))2 × L
2(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example
testifies the efficiency of the novel scheme. 相似文献
5.
对由定常非线性随机差分模型所定义状态空间为一般可测空间的离散时间随机系统,本文应用一般状态马氏链遍历性有关理论分析了系统的稳定性问题,给出了由系统相应确定性部分的Lyapunov函数来判别系统稳定的若干充分条件。 相似文献
6.
Xianmin Geng 《系统科学与复杂性》2011,24(2):218-224
There are a lot of continuous evolving networks in real world, such as Internet, www network, etc. The evolving operation
of these networks are not an equating interval of time by chance. In this paper, the author proposes a new mathematical model
for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of
degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution
of which counting process determines the operating number, and has proved that this system self-organizes into scale-free
structures with scaling exponent γ = 3+ α/m. 相似文献
7.
Hanying Liang 《系统科学与复杂性》2011,24(4):725-737
Consider heteroscedastic regression model Y
ni
= g(x
ni
) + σ
ni
ɛ
ni
(1 ≤ i ≤ n), where σ
ni
2 = f(u
ni
), the design points (x
ni
, u
ni
) are known and nonrandom, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors {ɛ
ni
, 1 ≤ i ≤ n} are assumed to have the same distribution as {ξ
i
, 1 ≤ i ≤ n}, which is a stationary and α-mixing time series with Eξ
i
= 0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g(·) and f(·). Finite sample behavior of the estimators is investigated via simulations, too. 相似文献
8.
This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using a new constructed Lyapunov function, the aggregation techniques, the Borne-Gentina practical stability criterion associated with the properties, new delay-independent stability conditions of the considered systems are established. Compared with the existing results in this area, the obtained result is explicit, simple to use and allows us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations, to demonstrate the effectiveness of the proposed method. 相似文献
9.
In this paper, under the constraint that the average distance and the average degree (k) remain approximately constant, we studied a random scale-free network model. We found that, if the network maintains the form of its degree distribution and the maximal degree kc is N-dependent cutoff function kc(N)〈 N, the degree distribution would be approximately power-law with an exponent between 2 and 3. The distribution exponent has little relationship with the average degree, denoted by (k). The diameter constraint can be interpreted as an environmental selection pressure, which could explain the scale-free nature of networks. The numerical results indicate that, under the diameter constraint, the preferential attachment can produce the cutoff function kc(N)〈 N and power-law degree distribution. 相似文献
10.
11.
<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space. 相似文献
12.
This paper considers a stochastic chemostat model with degenerate diffusion. Firstly, the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution. The authors show that the densities of the distributions of the solutions can converge in L1 to an invariant density. Then, conditions are obtained to guarantee the washout of the microorganism. Furthermore, through solving the corresponding Fokker-Planck equation, the authors give the exact expression of density function around the positive equilibrium of deterministic system. Finally, numerical simulations are performed to illustrate the theoretical results.
相似文献13.
This paper discusses the H
∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give
the basic theory about stabilities for such systems, including internal stability and external stability, which enables to
prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback
H
∞ control design is also extended to such systems. 相似文献
14.
Li XIA Chan ZHOU 《系统科学与复杂性》2007,20(1):18-29
In this paper, sequence unique reconstruction refers to the property that a sequence is uniquely reconstructable from all its K-tuples. We propose and study the phase transition behavior of the probability P(K) of unique reconstruction with regard to tuple size K in random sequences (iid model). Based on Monte Carlo experiments, artificial proteins generated from lid model exhibit a phase transition when P(K) abruptly jumps from a low value phase (e.g. 〈 0.1) to a high value phase (e.g. 〉 0.9). With a generalization to any alphabet, we prove that for a random sequence of length L, as L is large enough, P(K) undergoes a sharp phase transition when p ≤ 0.1015 where p = P (two random letters match). Besides, formulas are derived to estimate the transition points, which may be of practical use in sequencing DNA by hybridization. Concluded from our study, most proteins do not deviate greatly from random sequences in the sense of sequence unique reconstruction, while there are some "stubborn" proteins which only become uniquely reconstructable at a very large K and probably have biological implications. 相似文献
15.
This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations(PDEs) with non-constant(space-dependent) coefficients and different-type boundary conditions(BCs). The BCs could be heterogeneous-type or mixed-type.Specifically, this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for mixed-type. The main contribution is to extend PDE backstepping to the ... 相似文献
16.
<正> Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH~1-norm and L~2-norm are derived for the errors. 相似文献
17.
This paper investigates the inverse Lyapunov theorem for linear time invariant fractional order systems. It is proved that given any stable linear time invariant fractional order system, there exists a positive definite functional with respect to the system state, and the first order time derivative of that functional is negative definite. A systematic procedure to construct such Lyapunov candidates is provided in terms of some Lyapunov functional equations. 相似文献
18.
To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz’s, Chen’s and L¨u’s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit. 相似文献
19.
力矩平衡姿态的稳定性是空间站姿态TEA定向控制研究的重要问题.采用Lyapunov理论中求解导算子特征值的方法判断TEA的稳定性,基于线性化的姿态动力学方程采用基于稳定度设计的LQR方法设计空间站的姿态控制器,通过仿真验证了:(1)TEA作为平衡姿态的优点;(2)用导算子的特征值判断TEA姿态稳定性的方法的有效性. 相似文献
20.
The stabilization of switched linear systems with constrained inputs(SLSCI) is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time(MDT) to stabilized the system.First,for each subsystem with constrained inputs,a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system’s states lie inside this set.Then,by constructing a quadratic Lyapunov function for each closed-loop subsystem,an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system. 相似文献