asymptotic stability of impulsive stochastic partial differential equations with infinite delays in this paper we study the existence and asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay by employing a fixed point approach sufficient conditions are derived for achieving the required result these conditions do not require the monotone decreasing behaviour of the delays

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

stability analysis for fractional order advection reaction diffusion system abstract in this paper we present an alternative representation of the advection reaction diffusion model involving fractional order derivatives with mittag leffler kernel the study includes three main aspects existence and uniqueness of solutions hyers ulam stability and numerical simulations for the existence and uniqueness of solutions we use fixed point approach also we presents the hyers ulam stability for the numerical simulations a new numerical scheme that involve lagrange interpolation laplace transform and forward euler technique is considered numerical simulations were obtained for some specific parameters

on semi invariants and index for biparabolic seaweed algebras ii abstract in a continuation of i we study the semi invariant subalgebra sy q of s q for q a biparabolic subalgebra of a semisimple or of an affine lie algebra in most cases this is shown to be polynomial and we compute the degrees and weights of the generators we describe explicitly the canonical truncation q e of q for which sy q s q e q e let t denote the nilradical of q and q its derived algebra we show that the subalgebra s t q of s q q sy q is always polynomial and describe the degrees and weight of the generators finally a sum rule is given for the false degrees of s q q these are true degrees in most cases

double canonical bases abstract we introduce a new class of bases for quantized universal enveloping algebras u q g and other doubles attached to semisimple and kac moody lie algebras these bases contain dual canonical bases of upper and lower halves of u q g and are invariant under many symmetries including all lusztig s symmetries if g is semisimple it also turns out that a part of a double canonical basis of u q g spans its center and consists of higher casimirs which suggests physical applications

impulses induced p exponential input to state stability for a class of stochastic delayed partial differential equations abstractthis paper proposes a new stability concept called p exponential input to state stability piss for impulsive stochastic delayed partial differential equations isdpdes by employing the

the domain of attraction and the stability region for stochastic partial differential equations with delays abstract in this paper a stochastic partial differential equation with delays is considered on the basis of the properties of nonnegative matrices stochastic convolution and the inequality technique sufficient conditions for determining the domain of p th moment attraction and the p th moment asymptotic stability region are obtained an example is also discussed to illustrate the efficiency of the results obtained

on a stochastic evolution equation in a real separable hilbert space h where for every f 30 a t da c h h is a linear possibly unbounded operator v r 1a0 is a hilbert valued process of bounded variation m t a 0 is a hilbert valued locally square integrable martingale z t a o is a hilbert valued semimartingale and b c are operator valued functionals on the set of cadlag adapted hvalued processes b may be multivalued particular cases of i have been studied by many authors for example by arnold curtain kotelenez 11 chojnowska michalik 2 daletskii 4 da prato iannelli tubaro s 61 gyongy s ichikawa 9 lo kotelenez 14 151 krte 16 mahno 17 metivier 18 metivier pellaumail 193 metivier pistone 120 211 tubaro 23 tudor 24 25 krylov rozovskii 27 we propose conditions which insure the existence and the pathwise uniqueness for the mild solutions of i

boundary value problems for functional differential equations abstract this paper is concerned with the existence of solutions of a boundary value problem for second order functional differential equations specifically the following problem is considered x t f t x x t t in 0 t alpha 0 x 0 alpha 1 x 0 varphi in c r beta 0 x t beta 1 x t a in bbb r n the results are based on a nonlinear alternative of granas and the use of a priori bounds on solutions some examples are also discussed to illustrate how these results may be used to yield the existence of solutions of specific boundary value problems

existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii fixed point theorem the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions is studied the results are a generalization and continuation of the recent results on this issue an example is provided to illustrate the theory

pathwise global attractors for stationary random dynamical systems the asymptotic behaviour of random dynamical systems in polish spaces is considered under the assumption of existence of a random compact absorbing set assumption supposed to hold path by path a candidate pathwise attractora is defined the goal of the paper is to show that in the case of stationary dynamical systems a attracts bounded sets is measurable with respect to the algebra of invariant sets and is independent of when the system is ergodic an application to a general class of navier stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail

exponential stability for nonautonomous impulsive neutral partial stochastic evolution equations with delay abstractin this paper we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic ev

mean square stability of stochastic volterra integro differential equations abstract the mean square stability of a non linear stochastic volterra integro differential equation is studied non convolution volterra terms arise in both the drift and the dispersion term moreover for the convolution case we determine the rate of convergence in terms of an integrability condition on the volterra kernels

strong solutions to stochastic volterra equations in this paper stochastic volterra equations admitting exponentially bounded resolvents are studied after obtaining convergence of resolvents some properties for stochastic convolutions are studied our main results provide sufficient conditions for strong solutions to stochastic volterra equations

structured robust stability and boundedness of nonlinear hybrid delay systems taking different structures in different modes into account the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations sddes without the linear growth condition a new lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes moreover a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition

fixed points stability and exact linearization abstract we study the scalar equation x f t x x x b t g x t l 0 by means of contraction mappings conditions are obtained to ensure that each solution x t x t 0 0 as t the conditions allow f to grow as large as t but not as large as t 2 this is parallel to the classical result of smith quart j math oxford ser 12 2 1961 123 for the linear equation without a delay

existence and uniqueness attraction for stochastic age structured population systems with diffusion and poisson jump in this paper the problems about the existence and uniqueness attraction for strong solution of stochastic age structured population systems with diffusion and poisson jump are considered under the non lipschitz condition with the lipschitz condition being considered as a special case the existence and uniqueness for such systems is firstly proved by using the burkholder davis gundy inequality b d g inequality and ito s formula and then by using a novel inequality technique some sufficient conditions ensuring the existence for the domain of attraction are established as another by product the exponential stability in mean square moment of strong solution for such systems can be also discussed

boundary static output feedback control for nonlinear stochastic parabolic partial differential systems via fuzzy model based approach this article investigates a fuzzy boundary control problem of a class of stochastic nonlinear systems modeled by the ito type parabolic stochastic partial differential equation spde initially a takagi sugeno fuzzy spde model is proposed to accurately represent the nonlinear spde system then on the basis of the infinite dimensional infinitesimal operator a fuzzy boundary static output feedback controller is developed in terms of a set of linear matrix inequalities to locally exponentially stabilize the resulting system in the mean square sense by using an approximation argument and constructing a lyapunov function for the mild solution the local mean square exponential stability of the closed loop system is proved meanwhile the closed loop well posedness analysis is also given by virtue of the semigroup theory finally a simulation study on a belousov zhabotinsky reaction diffusion system with random parameter variation is presented to illustrate the effectiveness of the proposed method

the exponential stability for stochastic delay partial differential equations abstract in this paper we consider by the energy equality the exponential stability of energy solutions to a non linear stochastic functional partial differential equation with finite delay r 0 in separable hilbert spaces our method is very simple and is powerful for concrete stochastic delay partial differential equations

the existence and exponential stability of semilinear functional differential equations with random impulses under non uniqueness a b s t r a c t in this paper the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non uniqueness in a real separable hilbert space the results are obtained by using the leray schauder alternative fixed point theorem

stabilization of partially observed stochastic evolution systems abstract the stability of an evolution system with state dependent noise has been introduced by haussmann 7 and ichikawa 9 10 using a semigroup formulation of the model following a similar approach we study here the corresponding stabilization problem assuming partial observations under a convenient hypothesis we show the existence of a stabilizing control which is a linear feedback on the observation this result is established by extending the compensator concept to the stochastic case the theory is illustrated by a significant example

existence and exponential stability for impulsive stochastic partial functional differential equations in this paper the existence and uniqueness the exponential stability and the almost sure exponential stability of mild solution for impulsive stochastic partial functional differential equations with finite delay are considered some sufficient conditions are established for our concerned problems and some existing results are generalized and improved finally an illustrative example is provided to show the feasibility and effectiveness of the obtained results

stochastic functional evolution equations with monotone nonlinearity existence and stability of the mild solutions abstract in this paper we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition we prove the existence uniqueness and exponentially asymptotic stability of the mild solutions our approach is to apply a convenient version of burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in hilbert spaces an ito type inequality is the main tool to study the uniqueness p th moment and almost sure sample path asymptotic stability of the mild solutions we also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature

first order three point boundary value problems at resonance we consider three point boundary value problems for a system of first order equations in perturbed systems of ordinary differential equations at resonance we obtain new results for the above boundary value problems with nonlinear boundary conditions the existence of solutions is established by applying a version of brouwer s fixed point theorem which is due to miranda

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

stochastic nonhomogeneous incompressible navier stokes equations we construct solutions for 2 and 3 d stochastic nonhomogeneous incompressible navier stokes equations with general multiplicative noise these equations model the velocity of a mixture of incompressible fluids of varying density influenced by random external forces that involve feedback that is multiplicative noise weak solutions for the corresponding deterministic equations were first found by kazhikhov a v kazhikhov solvability of the initial and boundary value problem for the equations of motion of an inhomogeneous viscous incompressible fluid soviet phys dokl 19 6 1974 331 332 english translation of the paper in dokl akad nauk sssr 216 6 1974 1240 1243 a stochastic version with additive noise was solved by yashima h f yashima equations de navier stokes stochastiques non homogenes et applications thesis scuola normale superiore pisa 1992 the methods here extend the loeb space techniques used to obtain the first general solutions of the stochastic navier stokes equations with multiplicative noise in the homogeneous case m capinski n j cutland stochastic navier stokes equations applicandae math 25 1991 59 85 the solutions display more regularity in the 2d case the methods also give a simpler proof of the basic existence result of kazhikhov

a numerical algorithm for nonlinear multi point boundary value problems in this paper an algorithm is presented for solving second order nonlinear multi point boundary value problems bvps the method is based on an iterative technique and the reproducing kernel method rkm two numerical examples are provided to show the reliability and efficiency of the present method

existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup via monch fixed point abstract in this paper we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup in hilbert spaces sufficient conditions for the existence of mild solutions are obtained using the hausdorff measure of noncompactness and the monch fixed point theorem further we establish a new impulsive integral inequality to prove the exponential stability of mild solutions in the mean square moment finally an example is presented to illustrate our obtained results

existence and mean square exponential stability of mild solutions for impulsive stochastic partial differential equations with noncompact semigroup abstract in this paper with the help of the hausdorff measure of noncompactness the monch fixed point theorem and some inequality technique some new criteria to guarantee the mild solution for impulsive stochastic partial differential equations with varying time delays are obtained then by establishing a new impulsive integral inequality some sufficient conditions to ensure mean square exponential stability of mild solution for impulsive stochastic partial differential equations with varying time delays are obtained which will significantly improve some previous results 5 20 at last we give an example to illustrate the effectiveness and feasibility of the obtain results in our paper

quantum affine lie algebras casimir invariants and diagonalization of the braid generator let uq g be an infinite dimensional quantum affine lie algebra a family of central elements or casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation these eigenvalue formulas are shown to be absolutely convergent when the deformation parameter q is such that q 1 it is proven that the universal r matrix r of uq g satisfies the celebrated conjugation relation r tr with t the usual twist map as applications the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight uq g module and a spectral decomposition formula for the braid generator is obtained which is the generalization of reshetikhin s and gould s forms to the present affine case casimir invariants acting on a specified module are also constructed and their eigenvalues again absolutely convergent for q 1 computed by means of the spectral decomposition formula

stabilities in fdes by schauder s theorem abstract in a series of papers burton and furumochi dyn syst appl 10 2001 89 116 funkcial ekvac 44 2001 71 82 nonlinear anal 49 2002 445 454 dyn syst appl 11 2002 499 521 nonlinear stud to appear burton nonlinear stud 9 2002 181 190 furumochi qualitative theor differential equations to appear stability properties of solutions of fdes have been investigated by means of fixed point theory here we obtain new stability results for super linear fdes by using schauder s first theorem and a weighted norm and show some examples

on a third order multi point boundary value problem at resonance in this paper we prove some existence results for a third order multi point boundary value problem at resonance our method is based upon the coincidence degree theory of mawhin

optimal control of semilinear stochastic evolution equations the aim of this paper is to initiate a semigroup theory based approach to characterization of optimal markov controls for controlled semilinear stochastic evolution equations it may be recalled that markov controls are those that depend only on the current state at each time for finite dimensional controlled stochastic differential equations with a nondegenerate diffusion matrix this task is traditionally achieved through the hamilton jacobi bellman equation of dynamic programming associated with the problem and an accompanying verification theorem the latter states that an optimal markov control can be explicitly obtained by the pointwise minimization of a hamiltonian derivable from the solution of the hjb equation moreover any optimal markov control is obtainable in this manner

stability of semilinear stochastic evolution equations stability of moments of the mild solution of a semilinear stochastic evolution equation is studied and sufficient conditions are given for the exponential stability of the pth moment in terms of liapunov function sufficient conditions for sample continuity of the solution are also obtained and the exponential stability of sample paths is proved three examples are given to illustrate the theory

robustness of stability of nonlinear systems with stochastic delay perturbations abstract suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential functional equation in this paper a sufficient condition is given so that the perturbed system remains exponentially stable in the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable

large time behaviour for a class of turbulence models stochastic burgers equations the aim of this paper is to investigate large time behaviour i e stability and growth bounds of the solutions for a class of stochastic burgers equations the analysis is based on some robustness analysis involved with an infinite dimensional stochastic evolution equation various sufficient conditions for a stochastic burgers equation are obtained to ensure its asymptotic properties lastly several examples are given to illustrate our theory

feedback stabilization of some nonlinear stochastic systems on hilbert space has been considered by ichikawa lo where a generates a strongly continuous semigroup t t t 2 0 on a real separable hilbert space x f and g are nonlinear and satisfy lipschitz condition together with f 0 0 and g 0 0 that is f and g are bounded perturbations but in many practical situations f and g might be bounded or unbounded even uncertain that is f g e 6 where 6 is a family of nonlinear unbounded operators the problem of stabilization is to design a state feedback control law that assures exponential stability of the zero state uniformly with respect to perturbations f g e 6 this stabilization problem for perturbed uncertain linear systems in finite dimensions has received considerable attention in current literature 3 13 and references thereof we have considered similar problems for linear evolution equations in infinite dimensional spaces in our earlier work 14 151 in this paper we show that our approach can be extended to both deterministic and stochastic semilinear evolution equations based on perturbation theory of semigroups and some results of ichikawa furthermore in addition to exponential stability in the mean square sense for stochastic systems stability of sample paths is also obtained to our knowledge this problem involving infinite dimensional systems with unbounded and nonlinear perturbations has not been considered in the literature before

a stochastic extension of model reference adaptive control abstract a model reference adaptive control for the plant governed by linear stochastic differential equations is studied the controlled plant contains uncertainties in the coefficient an adaptive controller is designed to drive the distance between the distributions induced by the observation processes of the plant and its model to zero

stability in distribution of mild solutions to stochastic partial differential delay equations with jumps the existence uniqueness and some sufficient conditions for stability in distribution of mild solutions to stochastic partial differential delay equations with jumps are presented the principle technique of our investigation is to construct a proper approximating strong solution system and carry out a limiting type of argument to pass on stability of strong solutions to mild ones as a consequence stability results of basak et al basak et al 1999 j math anal appl 202 604 622 and yuan et al yuan et al 2003 syst control lett 50 195 207 are generalized to cover a class of much more general stochastic partial differential delay equations with jumps in infinite dimensions in contrast to the almost sure exponential stability in ichikawa ichikawa 1982 j math anal appl 90 12 44 and luo liu luo liu 2008 stoch proc appl 118 864 895 and the moment exponential stability in luo liu we present a new result on the stability in distribution of mild solutions finally an example is given to demonstrate the applicability of our work

stability results for stochastic delayed recurrent neural networks with discrete and distributed delays we present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays our approach is based on the method using fixed point theory which do not resort to any liapunov function or liapunov functional our results neither require the boundedness monotonicity and differentiability of the activation functions nor differentiability of the time varying delays in particular a class of neural networks without stochastic perturbations is also considered examples are given to illustrate our main results

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

almost sure asymptotic stability of stochastic partial differential equations with jumps in this paper we investigate stochastic partial differential equations with jumps in infinite dimensions the key motivation of this paper is under a local lipschitz condition but without a linear growth condition to give an existence and uniqueness theorem khasminskii type theorem where the classical existence and uniqueness result can be regarded as a special case and then to discuss the almost sure asymptotic stability of the solutions moreover as a by product we also derive that the solutions are weakly attracted finally several examples are constructed to demonstrate our results

fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays the fixed point theory is first used to consider the stability for stochastic partial differential equations with delays some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given these conditions do not require the monotone decreasing behavior of the delays which is necessary in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763 ruhollan jahanipur stability of stochastic delay evolution equations with monotone nonlinearity stoch anal appl 21 2003 161 181 even in this special case our results also improve the results in t caraballo k liu exponential stability of mild solutions of stochastic partial differential equations with delays stoch anal appl 17 1999 743 763

stabilization of some distributed parameter systems the question of stabilization of perturbed or uncertain infinite dimensional systems is considered one class of perturbations for which the system remains stabilizable by the same feedback law as for the nominal system is identified sufficient conditions are presented that generate strong stabilizability of the perturbed system given that the unperturbed system has similar properties it is also shown that for deterministic as well as stochastic systems exponential stability can be achieved by choice of a suitable feedback controller the theoretical results are illustrated by some numerical examples

improved stability conditions for a class of stochastic volterra levin equations in this paper we study the mean square asymptotic stability of a class of generalized nonlinear stochastic volterra levin equations by using fixed point theory several sufficient conditions are established for ensuring that the equation is mean square asymptotically stable as well as exponentially stable the main results are new which generalize and improve some well known results in burton 2006 4 and luo 2010 18 finally two examples are given to illustrate our results

absolute stability approach to stochastic stability of infinite dimensional nonlinear systems recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic this paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances our analysis is based on the lyapunov direct method to derive a stochastic lyapunov function we introduce the special stochastic infinite dimensional counterparts of the kalman yakubovich lemma they are proved by use of dynamic programming methods in combination with the properties of hilbert space valued wiener processes examples exhibit extensions of the popov and circle criteria to the feedback stochastic heat and delay equations respectively

braided doubles and rational cherednik algebras we introduce and study a large class of algebras with triangular decomposition which we call braided doubles braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational cherednik algebras we classify braided doubles in terms of quasi yetter drinfeld qyd modules over hopf algebras which turn out to be a generalisation of the ordinary yetter drinfeld modules to each braiding a solution to the braid equation we associate a qyd module and the corresponding braided heisenberg double this is a quantum deformation of the weyl algebra where the role of polynomial algebras is played by nichols woronowicz algebras our main result is that any rational cherednik algebra canonically embeds in the braided heisenberg double attached to the corresponding complex reflection group

robust stability and boundedness of nonlinear hybrid stochastic differential delay equations one of the important issues in the study of hybrid stochastic differential delay equations sddes is the automatic control with consequent emphasis being placed on the asymptotic analysis of stability and boundedness in the study of asymptotic properties the robust stability has received a great deal of attention the theory of robust stability shows how much perturbation a given stable hybrid sdde can tolerate so that its perturbed system remains stable almost all results so far on the robust stability require that the underlying sddes be either linear or nonlinear with linear growth condition however little is known on the robust stability of nonlinear hybrid sddes without the linear growth condition which is one of the key topics in this paper the other key topic is the robust boundedness the aim here is to answer the question how much perturbation can a given asymptotically bounded hybrid sdde tolerate so that its perturbed system remains asymptotically bounded

fixed points and exponential stability for stochastic volterra levin equations in this paper we study a stochastic volterra levin equation by using fixed point theory we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable our result generalizes and improves on the results in 14 1 30

exponential stability of a class of nonlinear systems via fixed point theory abstract in this paper the problem of globally stochastically exponential stability in the p th moment for a class of t s fuzzy stochastic impulsive genetic regulatory networks with random discrete delays distributed delays and parameter uncertainties is discussed by utilizing the theory of stochastic analysis semigroup theory and fixed point theory a novel sufficient condition to guarantee the globally stochastically exponential stability in the p th moment of the considered genetic regulatory networks is derived eventually an example is given to demonstrate that the obtained result is effective

the boundedness and stability of neutral delay differential equations with damped stochastic perturbations via fixed point theory in this paper a class of neutral stochastic differential equation is studied by using the fixed point method some conditions are established for ensuring the equation is bounded asymptotically stable and j c stable in mean square then with borel cantelli lemma several sufficient conditions for almost surely asymptotic stability and j c stability are given the conditions do not require the boundedness of delays nor do they ask for the continuousness on the coefficient functions the results of this paper are new and they extend and improve previously known results

square mean almost automorphic mild solutions to non autonomous stochastic differential equations in hilbert spaces in this paper we first refine the definition of square mean almost automorphic functions introduced in fu and liu 2010 11 then we prove the existence and uniqueness of square mean almost automorphic mild solutions for a class of non autonomous stochastic differential equations in a real separable hilbert space some additional properties of square mean almost automorphic functions are also provided to prove our main result we use the banach contraction mapping principle

solvability of functional differential equations with multi point boundary value problems at resonance in this paper we discuss the following third order functional differential equations x t f t x t fx t x t gx t x t hx t email protected 0 1 subject to the boundary conditions x 0 0 x 0 0 x 1 email protected email protected ix h i where f 0 1 xr email protected r f g h are three operators a i i 1 m 2 0 0 h 1 h 2 h m 2 1 under some appropriate conditions some existence and multiplicity results are given for the problem at resonance by using a priori estimates and the topological degree theory of mawhin

exponential stability of impulsive stochastic functional differential equations 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

stability of stochastic partial differential equations with infinite delays in this paper we study the existence and the asymptotical stability in p th moment of mild solutions to stochastic partial differential equations with infinite delays dx t ax t f t x t t t dt g t x t d t dw t t 0 x 0 x d f 0 b m 0 0 h where t t t t d t with delays t t d t as t our method for investigating the stability of solutions is based on the fixed point theorem

stability results for neutral stochastic functional differential equations via fixed point methods in this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle name

stability of stochastic partial differential equation stochastic partial differential equations such as occur in vibration problems for mechanical structures subjected to random loading are modelled as infinite dimensional stochastic ito differential equations using a semigroup approach sufficient conditions for exponential stability of the expected energy of the system as well as for the exponential decay of the sample paths of the displacement and velocity are given under these same conditions it is shown that the zero solution is pathwise asymptotically stable relative to finite dimensional initial conditions illustrative examples are included

stability of linear neutral differential equations with delays and impulses established by the fixed points method abstract in this paper we consider the impulsive effects on the stability of the zero solution of the linear neutral differential equations with variable delays by transforming the equations into ones without impulses and using fixed point theory some sufficient conditions for asymptotic stability and exponential stability of the zero solution are obtained the paper extends and improves results on sufficient conditions obtained by jin and luo 2008 17 and ardjouni and djoudi 2011 18 which is shown clearly in example 1 this paper also shows that the impulse intensity and the impulse time both influence the decay rate of the convergence to zero of the solutions finally two examples are given to show applications of some results obtained

asymptotic stability of second order neutral stochastic differential equations in this paper we study the existence and asymptotic stability in pth moment of mild solutions to second order nonlinear neutral stochastic differential equations further this result is extended to establish stability criterion for stochastic equations with impulsive effects with the help of fixed point strategy stochastic analysis technique and semigroup theory a set of novel sufficient conditions are derived for achieving the required result finally an example is provided to illustrate the obtained result

a new composition theorem for square mean almost automorphic functions and applications to stochastic differential equations abstract in this paper we establish a new composition theorem for square mean almost automorphic functions under conditions which are different from lipschitz conditions in the literature we apply this new composition theorem together with schauder s fixed point theorem to investigate the existence of square mean almost automorphic mild solutions for a stochastic differential equation in a real separable hilbert space finally an interesting corollary is also given for the sub linear growth cases

on discrete stochastic bilinear systems stability abstract mean square stability conditions for discrete time bilinear systems operating in a stochastic environment are given in this paper only independence and wide sense stationarity are required for the second order disturbance sequences involved thus dismissing ergodicity and zero mean assumptions stochastic stability conditions are derived by using a deterministic stability result for a class of separable nonlinear dynamical systems evolving in a banach space

on the exponential stability in mean square of neutral stochastic functional differential equations in 1 2 some efforts have been devoted to the investigation of exponential stability in mean square of neutral stochastic functional differential equations however the results derived there are either difficult to demonstrate in a straightforward way for practical situations or somewhat too restricted to be applied to general neutral stochastic functional differential equations for instance nonautonomous cases in this paper we shall establish some results which are more effective and relatively easy to verify to obtain the required stability