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1.
This paper is concerned with the existence of mild solutions for a class of impulsive fractional partial semilinear differential equations. Some errors in Mophou (2010) [2] are corrected, and some previous results are generalized.  相似文献   

2.
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   

3.
4.
The paper deals with the pathwise uniqueness of solutions to one-dimensional time homogeneous stochastic differential equations with a diffusion coefficient σ satisfying the local time condition and measurable drift term b. We show that if the functions σ and b satisfy a non-degeneracy condition and fundamental solution to considered equation is unique in law, then pathwise uniqueness of solutions holds. Our result is in some sense negative, more precisely we give an example of an equation with Holder continuous diffusion coefficient and nondegenerate drift for which a fundamental solution is not unique in law and pathwise uniqueness of solutions does not hold.  相似文献   

5.
Global results concerning stability properties of impulsive differential equations are established, employing piecewise continuous Lyapunov functions which are then applied for proving stability and boundedness properties  相似文献   

6.
In this paper, the stochastic asymptotical stability of stochastic impulsive differential equations is studied, and a comparison theory about the stochastic asymptotical stability of trivial solution is established. From the comparison theory, we can find out whether the stochastic impulsive differential system is stochastic asymptotically stable by studying the stability of a deterministic comparison system. As an application of this theory, we study the problem of chaos synchronization in Chua circuit using impulsive method. Finally, numerical simulation is employed to verify the feasibility of our method.  相似文献   

7.
In this paper, we investigate the existence of solutions of impulsive delay differential equation
  相似文献   

8.
In this paper, a class of stochastic functional differential equations given by
  相似文献   

9.
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties: randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.  相似文献   

10.
In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd) which denotes the family of bounded continuous Rd-value functions defined on (-∞,0] with norm under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation.  相似文献   

11.
The stability properties of stochastic differential equations with respetct to the perturbation of the coefficients and of the driving processes are investigated in the topology of uniform convergence in probability  相似文献   

12.
An approximation theorem of stochastic differential equations driven by semimartingales is proved, based on approximation of semimartingales by a sequence of processes with piecewise monotonic sample functions.  相似文献   

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14.
The standard existence and uniqueness theorem for stochastic differential equations requires Lipschitz condition of the coefficients. In this paper, we extend these results to the case in which the coefficients are not required to be Lipschitz continuous, instead they only satisfy a ‘weak’ type of Lipschitz condition.  相似文献   

15.
In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter , and a discontinuous drift. The proof of this result is based on the Girsanov theorem for the fractional Brownian motion.  相似文献   

16.
In this paper, we investigate a class of stochastic functional differential equations of the form
dx(t)=(Ax(t)+F(t,x(t),xt))dt+G(t,x(t),xtdW(t).  相似文献   

17.
In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.  相似文献   

18.
This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC((−∞,0];Rd). Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [t0,T]. Moreover, the existence-and-uniqueness theorem still holds on interval [t0,∞), where t0R is an arbitrary real number.  相似文献   

19.
In this paper, we study a system of nonlinear coupled wave equations with damping, source, and nonlinear strain terms. We obtain several results concerning local existence, global existence, and finite time blow‐up property with positive initial energy by using Galerkin method and energy method, respectively. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

20.
Global optimization and stochastic differential equations   总被引:5,自引:0,他引:5  
Let n be then-dimensional real Euclidean space,x=(x 1,x 2, ...,x n)T n , and letf: n R be a real-valued function. We consider the problem of finding the global minimizers off. A new method to compute numerically the global minimizers by following the paths of a system of stochastic differential equations is proposed. This method is motivated by quantum mechanics. Some numerical experience on a set of test problems is presented. The method compares favorably with other existing methods for global optimization.This research has been supported by the European Research Office of the US Army under Contract No. DAJA-37-81-C-0740.The third author gratefully acknowledges Prof. A. Rinnooy Kan for bringing to his attention Ref. 4.  相似文献   

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