共查询到20条相似文献,搜索用时 31 毫秒
1.
本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解. 相似文献
2.
In this paper,we investigate the stability of the split-step theta(SST)method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations(NSDDEs)with Markov switching and jumps.As we know,there are few results on the stability of numerical solutions for NSDDEs with Markov switching and jumps.The purpose of this paper is to enrich conclusions in such respect.It first devotes to show that the trivial solution of the NSDDE with Markov switching and jumps is exponentially mean square stable and asymptotically mean square stable under some suitable conditions.If the drift coefficient also satisfies the linear growth condition,it then proves that the SST method applied to the NSDDE with Markov switching and jumps shares the same conclusions with the exact solution.Moreover,a numerical example is demonstrated to illustrate the obtained results. 相似文献
3.
In this paper, we are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory’s approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the Lp-norm when the drift and diffusion coefficients are Taylor approximations. 相似文献
4.
A problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching and random diffusion (noise) is considered. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. Sufficient conditions based on linear matrix inequalities (LMI's) for stochastic stability is obtained. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results. 相似文献
5.
Wenrui
Li Ming Ye Qimin Zhang Yan Li 《Numerical Methods for Partial Differential Equations》2020,36(6):1460-1491
In this paper, a stochastic age-structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age-structured population system in a polluted environment. 相似文献
6.
This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential
equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of
classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability
criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived
for the continuous problem. It is found that, under suitable conditions, these two classes of numerical methods retain the
stability of the continuous systems. Some numerical examples are given that illustrate the theoretical results.
This research is supported by Fellowship F/02/019 of the Research Council of the K.U.Leuven, NSFC (No.10571066) and SRF for
ROCS, SEM. 相似文献
7.
研究了一类带Markov状态转换的跳扩散方程的数值解的问题,为讨论这类方程精确解的数值计算问题,我们给出了一种基于Euler格式的方程解的跳适应算法,并在一定的条件下,证明了基于这种新的跳适应算法所得到的方程的数值解是收敛于它的精确解,同时还给出了数值解收敛到其精确解的收敛阶数.最后,本文通过两个例子说明了这种跳适应算法的计算有效性. 相似文献
8.
《Numerical Methods for Partial Differential Equations》2018,34(3):1033-1052
We introduce and analyze a strongly stable numerical method designed to yield good performance under challenging conditions of irregular or mismatched initial data for solving systems of coupled partial integral differential equations (PIDEs). Spatial derivatives are approximated using second order central difference approximations by treating the mixed derivative terms in a special way. The integral operators are approximated using one and two–dimensional trapezoidal rule on an equidistant grid. Computational complexity of the method for solving large systems of PIDEs is discussed. A detailed treatment for the consistency, stability, and convergence of the proposed method is provided. Two asset American option under regime–switching with jump–diffusion model when solved using a penalty term, leads to a system of two dimensional PIDEs with mixed derivatives. This model involves double probability density function which brings more challenges to the numerical solution in already a complicated partial integral differential equation. The complexity of the dense jump probability generator, the nonlinear penalty term and the regime–switching terms are treated efficiently, while maintaining the stability and convergence of the method. The impact of the jump intensity and other parameters is shown in the graphs. Numerical experiments are performed to demonstrated efficiency, accuracy, and reliability of the proposed approach. 相似文献
9.
耿晓晶 《纯粹数学与应用数学》2013,(6):646-653
由于多维马尔科夫转制随机微分方程不存在解析解,利用Euler—Maruyama方法给出多维马尔科夫转制随机微分方程的渐进数值解,并证明了此数值解收敛到方程的解析解.将单一马尔科夫转制随机微分方程的数值解问题延伸到多维马尔科夫转制情形,增强了马尔科夫转制随机微分方程的适用性. 相似文献
10.
p-Moment Stability of Stochastic Nonlinear Delay Systems with Impulsive Jump and Markovian Switching
Zaiming Liu 《随机分析与应用》2013,31(5):911-923
Abstract This article is concerned with the problem of p-moment stability of stochastic differential delay equations with impulsive jump and Markovian switching. In this model, the features of stochastic systems, delay systems, impulsive systems, and Markovian switching are all taken into account, which is scarce in the literature. Based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain new criteria ensuring p-moment stability of trivial solution of a class of impulsive stochastic differential delay equations with Markovian switching. 相似文献
11.
G. Yin 《Journal of Theoretical Probability》2001,14(3):673-697
This work is devoted to the weak convergence analysis of a class of aggregated processes resulting from singularly perturbed switching diffusions with fast and slow motions. The processes consist of diffusion components and pure jump components. The states of the pure jump component are naturally divisible into a number of classes. Aggregate the states in each weakly irreducible class by a single state leading to an aggregated process. Under suitable conditions, it is shown that the aggregated process converges weakly to a switching diffusion process whose generator is an average with respect to the quasi-stationary distribution of the jump process. 相似文献
12.
Albert C.J. Luo Yang Wang 《Communications in Nonlinear Science & Numerical Simulation》2009,14(8):3472-3485
In this paper, the switching dynamics of linear oscillators with arbitrary discontinuous forcing are investigated through the concept of switching systems, and such switching systems consist of countable prescribed linear oscillators with different external excitations. The traditional treatments are to smoothen the discontinuity at switching points of two subsystems in a switching system, which can provide an approximate solution only. Therefore, an alternative method is presented to obtain an exact solution of the resultant switching linear system. Under periodic piecewise forcing and random forcing, the corresponding exact solutions and stochastic responses of switching linear systems are developed. For any periodic forcing, the periodic responses and stability of the resultant system composed of multiple linear oscillators in different time intervals are presented. In addition, the resultant switching system consisting of two oscillators are discussed, and the corresponding stability analysis is carried out. 相似文献
13.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(6):1000-1032
This work develops Feynman–Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated with a general Lévy process and the switching part depends on the jump diffusion processes. Under broad conditions, the connections of such stochastic processes and the corresponding partial integro-differential equations are established. Related initial, terminal and boundary value problems are also treated. Moreover, based on weak convergence of probability measures, it is demonstrated that a sequence of random variables related to the regime-switching jump diffusion process converges in distribution to the arcsine law. 相似文献
14.
The p-th moment and almost sure stability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two examples are provided to support the conclusions. 相似文献
15.
16.
This paper deals with asymptotical
stability in probability in the large for stochastic bilinear
systems. Some new criteria for asymptotical stability of such
systems have been established in the inequality of mathematic
expectation. A sufficient condition for bilinear stochastic jump
systems to be asymptotically stable in probability in the large in
Markovian switching laws is derived in a couple of Riccati-like
inequalities by introducing a nonlinear state feedback controller.
An illustrative example shows the effectiveness of the method. 相似文献
17.
A problem of robust guaranteed cost control of stochastic discrete-time systems with parametric uncertainties under Markovian switching is considered. The control is simultaneously applied to both the random and the deterministic components of the system. The noise (the random) term depends on both the states and the control input. The jump Markovian switching is modeled by a discrete-time Markov chain and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Using linear matrix inequalities (LMIs) approach, the robust quadratic stochastic stability is obtained. The proposed control law for this quadratic stochastic stabilization result depended on the mode of the system. This control law is developed such that the closed-loop system with a cost function has an upper bound under all admissible parameter uncertainties. The upper bound for the cost function is obtained as a minimization problem. Two numerical examples are given to demonstrate the potential of the proposed techniques and obtained results. 相似文献
18.
This paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching. The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix. New criteria for testing the robust stability of such systems are established in terms of bi-linear matrix inequalities (BLMIs), and sufficient conditions are proposed for the design of robust state-feedback controllers. A numerical example is given to illustrate the effectiveness of our results. 相似文献
19.
This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method. 相似文献
20.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(2):798-804
In this paper, we are concerned with the stochastic differential delay equations with Poisson jump (SDDEsPJ). As stochastic differential equations, most SDDEsPJ cannot be solved explicitly. Therefore, numerical solutions have become an important issue in the study of SDDEsPJ. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJ when the drift and diffusion coefficients are Taylor approximations. 相似文献