Last edited by Akihn
Friday, November 6, 2020 | History

4 edition of Exponential stability of stochastic differential equations found in the catalog.

# Exponential stability of stochastic differential equations

Written in English

Subjects:
• Stochastic differential equations.,
• Delay differential equations.

• Edition Notes

Includes bibliographical references (p. 295-304) and index.

Classifications The Physical Object Statement Xuerong Mao. Series Monographs and textbooks in pure and applied mathematics ;, 182 LC Classifications QA274.23 .M35 1994 Pagination xii, 307 p. : Number of Pages 307 Open Library OL1082426M ISBN 10 0824790804 LC Control Number 94006019

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper is concerned with the exponential stability of nontrivial solutions of stochastic differential equations. In this paper, we give new criteria for the exponential stability for stochastic differential equations without the trivial solution. Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay. Abstract. The stochastic -method is extended to solve nonlinear stochastic Volterra integro-differential mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochastic -method is convergent of order in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability Cited by: 3. S. Zhou and M. Xue, “The existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay,” Journal of Applied Mathematics, vol. 1, pp. 95–, View at: Google Scholar; X. Mao, Stochastic Differential Equations and Their Applications, Horwood Publication, Chichester, UK, Cited by: 1.

You might also like
Kyahna region land utilization and occupancy study

Kyahna region land utilization and occupancy study

Lure of the limerick

Lure of the limerick

Physics 6A, statics and dynamics

Physics 6A, statics and dynamics

How to study

How to study

Essentials of learning for instruction

Essentials of learning for instruction

Price theory in action.

Price theory in action.

The pathways to the diploma program

The pathways to the diploma program

Documentation, 1974-75, with an overview of the program and additions from 1975-76

Documentation, 1974-75, with an overview of the program and additions from 1975-76

Gathering to Nauvoo

Gathering to Nauvoo

The wild tribes in Indian history

The wild tribes in Indian history

Representative projects

Representative projects

### Exponential stability of stochastic differential equations by Xuerong Mao Download PDF EPUB FB2

: Exponential Stability of Stochastic Differential Equations (Chapman & Hall Pure and Applied Mathematics) (): Mao, Xuerong: BooksCited by: Mao, Xuerong () Exponential stability of stochastic differential equations.

Marcel Dekker. ISBN Full text not available in this repository. Abstract. This unique, self-contained reference presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators - detailing various exponential stabilities for stochastic Cited by: Get this from a library.

Exponential stability of stochastic differential equations. [Xuerong Mao] -- This unique, self-contained reference presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators - detailing various exponential.

ISBN: OCLC Number: Notes: Literaturverz. - Description: XII, Seiten Diagramme: Contents: Semimartingales with Spatial Parameters and Stochastic Integrals; Stochastic Differential Equations; Stochastic Differential Delay Equations; Exponential Stability of Stochastic Differential Equations; Almost Sure Exponential Stability of Stochastic.

Abstract. This paper systematically investigates the exponential stability of the solution for $$I\hat{t}o$$ equations, presenting the comparison criterions of stochastic exponential stability, exponential p-stability and almost surely exponential stability. These comparison criterions generalize the corresponding research results by Nevel’son and Has’: Hong-ke Wang.

Deﬁnition of stochastic stability Diffusion operator It turns out that there are various different types of stochastic stability. In this course, we will only concentrate on stability in probability; pth moment exponential stability; almost sure exponential stability.

Xuerong Mao FRSE Stability of SDE. In this section, we consider the exponential stability for G-stochastic differential equations. Firstly, given an exponentially stable stochastic linear system () { d X t = A X t d t, t ≥ t 0 ≥ 0, X t 0 = X 0, t 0 ≥ 0, where the initial condition X 0 ∈ L G 2 (Ω t 0 ; R n), X = (X 1,X n) T, A is a constant n × n Cited by: Exponential stability of the stochastic θ-method Exponential stability of stochastic differential equations book stochastic differential equations with G-Brownian motion (called G-SDEs for brevity) is investigated.

It is proved that under the global Lipschitz condition, a G-SDE is p th (p ∈ (0, 1)) moment exponentially stable if and only if the stochastic θ -method with a sufficiently small step size is also p th moment exponentially by: 4.

The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability Exponential stability of stochastic differential equations book and linear matrix inequalities (LMIs).

brilliant books of Øksendal () and Karatzas and Shreve (). 3 Itô Calculus and Stochastic Differential Equations 31 Note that the matrix exponential cannot be computed by computing scalar expo-nentials of the individual File Size: 1MB.

By applying stochastic processes theory, stochastic analysis theory and Lyaponov method, we establish several novel exponential stability criteria of the suggested system.

Finally, several simple examples are provided to show the validity and significance of the by: 1. In this paper, we shall discuss p th moment exponential stability of the following nonlinear neutral stochastic delay differential equations with Markovian switching: () d [x (t) − C (t) x (t − τ)] = f (x (t), x (t − τ), t, r (t)) d t + g (x (t), x (t − τ), t, r (t)) d ω (t), on t ≥ 0 with the initial data x 0 = φ = {φ (θ), − τ ≤ θ ≤ 0} ∈ C F 0 p ([− τ, 0]; R d), C (t) ∈ C ([0, ∞); R d × d).Cited by: A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic are used to model various phenomena such as unstable stock prices or physical systems subject to thermal lly, SDEs contain a variable which represents random white.

Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients.

The exponential stability in the p th moment for mild solution to neutral stochastic fractional integro-differential equations with Poisson jump is Cited by: 2. Abstract. The main purpose of this chapter is to study the stability problem for stochastic partial differential equations (SPDE).

The exponential stability in the mean square sense of the mild and strong solutions of linear SPDE was undertaken in a systematic manner by Haussman [3] and was continued by Chow [1].Cited by: () Almost sure exponential stability of hybrid stochastic functional differential equations.

Journal of Mathematical Analysis and ApplicationsCited by: order to stabilize unstable di erential equations. Key words: Almost sure exponential stability, stochastic di erential delay equa-tions, It^o formula, Brownian motion, stochastic stabilization.

AMS subject classi cations: 60H10, 60J10, 93D 1 Introduction It is very easy to show that the linear scalar stochastic di erential equation (SDE). The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method Cited by: () Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

Journal of Inequalities and Applications () The partially truncated Euler–Maruyama method and its stability and by: The aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d[ x (t) − G (x t)] = [ f (t, x (t)) + g (t, x t)]d t + σ (t, x t)d w (t), where x t = { x (t + s): − τ ⩽ s ⩽ 0}, with τ > 0, is the past history of the by: Boundedness and exponential stability of highly nonlinear stochastic differential equations Article (PDF Available) in Electronic Journal of Differential Equations.

general stochastic functional differential equations has been extensively studied by Mao in a series of books and articles (see [13], [14], [16], and the references therein).

The theory is much less well developed in the case where the driving noise has jumps. Citation: Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang.

pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state te & Continuous Dynamical Systems - B,22 (1): doi: /dcdsbCited by: 1.

Robustness of exponential stability of stochastic differential delay equations Article (PDF Available) in IEEE Transactions on Automatic Control 41(3) - April with Reads. ter V we use this to solve some stochastic diﬁerential equations, including the ﬂrst two problems in the introduction.

In Chapter VI we present a solution of the linear ﬂltering problem (of which problem 3 is an example), using the stochastic calculus. Problem 4 is the Dirichlet problem. Although this isFile Size: 1MB.

() Exponential stability of neutral stochastic differential functional equations with Markovian switching. International Conference on Machine Learning and Cybernetics, () Mean square asymptotic stability of stochastic delayed systems by Cited by: We regard the stochastic functional differential equation with infinite delay dx(t)=f(xt)dt+g(xt)dw(t) as the result of the effects of stochastic perturbation to the deterministic functional differential equation ẋ(t)=f(xt), where.

Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations 1 X. Liao 2 and X. Mao 3 Department of. Stability conditions for functional differential equations can be obtained using Lyapunov functionals.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with work continues and complements the author’s previous book Cited by: () Choice of θ and mean-square exponential stability in the stochastic theta method of stochastic differential equations.

Journal of Computational and Applied Mathematics() The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential by: Stochastic Diﬀerential Equations (SDE) When we take the ODE (3) and assume that a(t) is not a deterministic parameter but rather a stochastic parameter, we get a stochastic diﬀerential equation (SDE).

The stochastic parameter a(t) is given as a(t) = f(t) + h(t)ξ(t), (4) where ξ(t) denotes a white noise process. Thus, we obtain dX(t) dt. p th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay Abstract: The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state by:   Abstract.

In this paper, BDG-type inequality for G-stochastic calculus with respect to G-Lévy process is obtained, and solutions of the stochastic differential equations driven by the G-Lévy process under the non-Lipschitz condition are rmore, the mean square exponential stability and quasi-sure exponential stability of the solution using the G Author: Bingjun Wang, Hongjun Gao.

probability space. The stochastic (m−1)-vector process B consists of jointly independent Wiener processes Mathematics Subject Classiﬁcation.

34K50, 34D Key words and phrases. Stochastic diﬀerential equations, aftereﬀect, exponential stability, integral transforms.

EJQTDE, No. 23, p. A novel approach for designing the feedback control based on past states is proposed for hybrid stochastic differential equations (SDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of hybrid SDEs.

Department of Mathematics, Anhui Normal University, WuhuAnhui, China, China. Department of Mathematics, Anhui Normal University, WuhuAnhui, ChinaCited by:   This paper considers fractional stochastic differential equations with distributed delay.

With the variation-of-constants formula, an explicit expression and asymptotic behavior of the solution are provided, sufficient conditions are derived to guarantee the p th moment exponential stability and almost surely exponential by: 3.

Citation: Min Zhu, Panpan Ren, Junping Li. Exponential stability of solutions for retarded stochastic differential equations without dissipativity.

Discrete & Continuous Dynamical Systems - B,22 (7): doi: /dcdsbAuthor: Min Zhu, Panpan Ren, Junping Li. Abstract. In this paper, we consider the stability in pth moment of mild solutions to nonlinear impulsive stochastic delay partial differential equations (NISDPDEs).By employing a fixed point approach, sufficient conditions for the exponential stability in pth moment of Author: Lei Zhang, Yongsheng Ding, Tong Wang, Liangjian Hu, Kuangrong Hao.

Stochastic Stability of Differential Equations (Stochastic Modelling and Applied Probability Book 66) - Kindle edition by Khasminskii, Rafail, Milstein, Grigori Noah. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Stochastic Stability of Differential Equations (Stochastic 5/5(1).This paper establishes exponential mean square stability of two classes of theta Milstein methods, namely split-step theta Milstein (SSTM) method and stochastic theta Milstein (STM) method, for stochastic differential delay equations (SDDEs).Cited by: 2.THE EXPONENTIAL STABILITY OF NEUTRAL STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS T.

Caraballo 1, J. Real, & T. Taniguchi2 1 Departamento de Ecuaciones Diferenciales y An´alisis Num´erico, Universidad de Sevilla, Apdo.

de Correos–Sevilla, Spain 2 Division of Mathematical Sciences, Graduate School of Comparative .