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1.
In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.  相似文献   

2.
We consider the problem of minimizing a polynomial over a set defined by polynomial equations and inequalities. When the polynomial equations have a finite set of complex solutions, we can reformulate this problem as a semidefinite programming problem. Our semidefinite representation involves combinatorial moment matrices, which are matrices indexed by a basis of the quotient vector space ℝ[x 1, . . . ,x n ]/I, where I is the ideal generated by the polynomial equations in the problem. Moreover, we prove the finite convergence of a hierarchy of semidefinite relaxations introduced by Lasserre. Semidefinite approximations can be constructed by considering truncated combinatorial moment matrices; rank conditions are given (in a grid case) that ensure that the approximation solves the original problem to optimality. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.  相似文献   

3.
We consider L -norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.  相似文献   

4.
Postnov  S. S. 《Doklady Mathematics》2017,96(2):531-534

Two optimal control problems are studied for linear stationary systems of fractional order with lumped variables whose dynamics is described by equations with Hadamard derivative, a minimum-norm control problem and a time-optimal problem with a constraint on the norm of the control. The setting of the problem with nonlocal initial conditions is considered. Admissible controls are sought in the class of functions p-integrable on an interval for some p. The main approach to the study is based on the moment method. The well-posedness and solvability of the moment problem are substantiated. For several special cases, the optimal control problems under consideration are solved analytically. An analogy between the obtained results and known results for systems of integer and fractional order described by equations with Caputo and Riemann–Liouville derivatives is specified.

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5.
《随机分析与应用》2013,31(6):1281-1307
The paper is devoted to the generalized stochastic differential equations of the Ito? type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions.  相似文献   

6.
Guangjie Li 《Applicable analysis》2018,97(15):2555-2572
Little seems to be known about stability results on the neutral stochastic function differential equations with Markovian switching driven by G-Brownian (G-NSFDEwMSs). This paper aims at investigating the pth moment exponential stability for G-NSFDEwMSs to fill this gap. Some sufficient conditions on the pth moment exponential stability of the trivial solution are derived by employing the Razumikhin-type method, stochastic analysis, and algebraic inequality technique. Moreover, an example is provided to illustrate the effectiveness of the obtained results.  相似文献   

7.
This article considers a class of nonlocal stochastic functional differential equations with infinite delay whose coefficients are dependent the pth moment and establishes the existence-and-uniqueness theorem under the conditions that are similar to the classical linear growth condition and the Lipschitz condition. Compared with the existing results, the conditions of this article are easier to test.  相似文献   

8.
The main aim of this paper is to study the stability of the stochastic functional differential equations with infinite delay. We establish several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations with infinite delay. By applying these results to stochastic differential equations with distributed delay, we obtain some sufficient conditions for both pth moment and almost surely exponentially stable. Finally, some examples are presented to illustrate our theory.  相似文献   

9.
The perturbed Sparre Andersen model with a threshold dividend strategy   总被引:1,自引:0,他引:1  
In this paper, we consider a Sparre Andersen model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the mth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber–Shiu functions. The special case where the inter-claim times are Erlang(2) distributed and the claim size distribution is exponential is considered in some details.  相似文献   

10.
11.
In this paper, we investigate the αth moment asymptotical stability of the analytic solution and the numerical methods for the stochastic pantograph equation by using the Razumikhin technique. Especially the linear stochastic pantograph equations and the semi-implicit Euler method applying them are considered. The convergence result of the semi-implicit Euler method is obtained. The stability conditions of the analytic solution of those equations and the numerical method are given. Finally, some experiments are given.  相似文献   

12.
Since Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities.  相似文献   

13.
In this paper, we study the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic partial functional integrodifferential equations with delays. We suppose that the linear part possesses a resolvent operator in the sense given in Grimmer [R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc. 273(1) (1982), 333–349] and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is employed for achieving the required result. An example is provided to illustrate the results of this work.  相似文献   

14.
Algebraic polynomials that occur in the generalized moment representation of a specified number sequence are found in the form of linear combinations of orthogonal polynomials. The coefficients of these linear combinations are computed from a system of algebraic equations and the polynomials that are found satisfy integral and differential equations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 995–997, July, 1992.  相似文献   

15.
In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case.  相似文献   

16.
The study of moment functions on commutative topological groups leads to the study of systems of functional equations. Systems of functional equations characterizing moment functions and sequences of moment functions are closely related to exponential functions and additive functions. Here we describe moment functions and generalized moment functions on polynomial hypergroups.Received: 23 May 2003; revised: 20 September 2004  相似文献   

17.
We prove exponential rates of convergence of a class of hp Galerkin Finite Element approximations of solutions to a model tensor nonhypoelliptic equation in the unit square □ = (0, 1)2 which exhibit singularities on ?□ and on the diagonal Δ = {(x, y) ∈ □ : x = y}, but are otherwise analytic in □. As we explained in the first part (Pentenrieder and Schwab, Research Report, Seminar for Applied Mathematics, 2010) of this work, such problems arise as deterministic second moment equations of linear, second order elliptic operator equations Au = f with Gaussian random field data f. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012  相似文献   

18.
Abstract

This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p > 2).  相似文献   

19.
In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay.  相似文献   

20.
Rheological relationships linking mean and moment stresses and, also, the force and moment of interphase reaction in a macroscopic flow of small solid sphere suspension with the kinematic characteristics of the flow are derived. This makes it possible to close the system of equations of suspension hydrodynamics. Coefficients of viscosity and of moment viscosity of a suspension are obtained and calculated.The equations of conservation of mass, momentum and moment of momentum of suspension and of its phases, considered (from the macroscopic point of view) to be coexistent continuous media, were formulated in a general form in [1]. These equations contain unknown vectors and tensors which define the interaction between the considered continuous media and, also, stresses and moment stresses appearing when these are in motion. To close the equations of conservation it is necessary to express all these quantities in terms of unknown variables of these equations (mean concentration of suspension, pressure in the fluid phases, and phase velocities). This problem is the second of the fundamental problems of hydromechanics of suspensions indicated in [1].Here this problem is solved with the use of a kind of self-consistent field theory, which is essentially an extension and generalization of methods developed in [2 – 7]. Expressions for all of the quantities mentioned above are derived. They can be considered to be rheological equations of state for suspensions. Expressions for the various coefficients of these equations and their dependence on parameters of phases and on the flow frequency spectrum are also considered.  相似文献   

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