decay rate dependent conditions for exponential stability of stochastic neutral systems with markovian jumping parameters abstract this note studies the problem of decay rate dependent exponential stability for neutral stochastic delay systems with markovian jumping parameters first by introducing an operator d x t i as well as a novel lyapunov krasovskii functional sufficient conditions for exponential stability of system with a decay rate are obtained second the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with markovian jumping parameters finally numerical examples are provided to show the effectiveness of the proposed results

stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

on the asymptotic behavior for neutral stochastic differential delay equations this note investigates the existence and uniqueness as well as the stability of the general decay rate of the global solution for neutral stochastic differential equations with time varying delay under a locally lipschitz condition a contractive condition and a monotonicity condition the stability results are derived by using the lyapunov function approach and some stochastic analysis techniques which not only cover the exponential stability in the p th p 0 moment and the almost sure exponential stability but also the polynomial stability in the p th p 0 moment and the almost sure polynomial stability two examples including one coupled system consisting of a mass spring damper connected to a pendulum and the nonlinear external random force are given to illustrate the effectiveness of the obtained results

subelliptic peter weyl and plancherel theorems on compact connected semisimple lie groups abstract we will study the connections between the elliptic and subelliptic versions of the peter weyl and plancherel theorems in the case when the sub riemannian structure is generated naturally by the choice of a cartan subalgebra along the way we will introduce and study the subelliptic casimir operator associated to the subelliptic laplacian

brief paper robustness of exponential stability of a class of stochastic functional differential equations with infinite delay we regard the stochastic functional differential equation with infinite delay dx t f x t dt g x t dw t as the result of the effects of stochastic perturbation to the deterministic functional differential equation email protected t f x t where x t x t q c 0 r n is defined by x t q x email protected email protected 0 we assume that the deterministic system with infinite delay is exponentially stable in this paper we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable

on energy inequality smoothness and large time behavior in l 2 for weak solutions of the navier stokes equations in exterior domains soit un domaine exterieur de r n n 3 4 a frontiere lisse sur le cylindre d espace temps 0 on considere le probleme de navier stokes non stationnaire u t u u u p f dans 0 u 0 dans 0 u 0 sur 0 u x 0 a x avec des donnees prescrites f et a

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

the improved lasalle type theorems for stochastic functional differential equations abstract the main aim of this paper is to improve some results obtained by mao x mao the lasalle type theorems for stochastic functional differential equations nonlinear stud 7 2000 307 328 our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above for example we need only the local lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions to guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation sfde under the weaker conditions imposed in this paper we establish a generalised existence and uniqueness theorem which covers a wider class of nonlinear sfdes as demonstrated by the examples discussed in this paper moreover from our improved results follow some new criteria on the stochastic asymptotic stability for sfdes

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

stochastic lotka volterra population dynamics with infinite delay we discover in this paper that when environmental noise is strongly dependent on the population size this noise may suppress the population explosion in a finite time and guarantee the global positive solution when the environmental noise is weakly dependent on the population size the conditions that guarantee the global positive solution are independent of this environmental noise we also discuss the pth moment boundedness stochastic ultimate boundedness and moment average boundedness in time under two classes of conditions these properties are natural requirements from the biological point of view

the almost sure asymptotic stability and p th moment asymptotic stability of nonlinear stochastic differential systems with polynomial growth this note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems sdss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such sdss we also provide the range of the order p a numerical example is provided to illustrate the effectiveness and the benefits of the proposed result

algebraic l 2 decay for weak solutions of a viscous boussinesq system in exterior domains abstract the algebraic decay rates for the total kinetic energy of weak solutions of the n dimensional viscous boussinesq system in exterior domains are established by means of the spectral decomposition method of fractional powers of the laplacian and stokes operators the results reveal that l 2 decay of the velocity field with zero divergence becomes slower than that of the temperature

noise suppresses or expresses exponential growth in this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially on the other hand we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially in other words we reveal that the noise can suppress or expresses exponential growth

asymptotic behavior for the navier stokes equations in 2d exterior domains we show that the lp spatial temporal decay rates of solutions of incompressible flow in an 2d exterior domain when a domain has a boundary pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary to overcome the difficulty we adopt the ideas in he xin c he z xin weighted estimates for nonstationary navier stokes equations in exterior domain methods appl anal 7 3 2000 443 458 and our previous results h o bae b j jin asymptotic behavior of stokes solutions in 2d exterior domains j math fluid mech in press h o bae b j jin temporal and spatial decay rates of navier stokes solutions in exterior domains submitted for publication for the spatial decay rate estimate we first extend temporal decay rate result of the navier stokes solutions for general lp space when the initial velocity is in l 2 lr 1 r q 1 r q

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

on the regularity of subelliptic p harmonic functions in carnot groups abstract in this paper we prove second order horizontal differentiability and c 1 regularity results for subelliptic p harmonic functions in carnot groups for p close to 2

weighted estimates for the incompressible fluid in exterior domains for a strong solution u x t of the navier stokes equations in exterior domain in rn where n 2 3 we study the time decay of x u t lp for n when a domain has a boundary pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary to overcome the difficulty we adopt the ideas in h o bae b j jin temporal and spatial decay rates of navier stokes solutions in exterior domains bull korean math soc 44 3 2007 547 567 h o bae b j jin asymptotic behavior for the navier stokes solutions in 2d exterior domains j funct anal 240 2006 508 529 and we will extend bae and jin s results by modifying their methods

exponential stability in mean square of neutral stochastic differential functional equations abstract 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 xt f t x t g t xt dt t xt dw t where xt x t s s 0 with 0 is the past history of the solution several interesting examples are a given for illustration

exponential stability of singularly perturbed stochastic systems the sufficient conditions of exponential stability of singularly perturbed nonlinear stochastic systems are established the excitations are assumed to be parametric white noises in this case the objective is to analyze the full order system in their lower order subsystems i e the reduced order system and the boundary layer system and in terms of their interconnecting structure and the perturbation parameter varepsilon the exponential bounds depend on the moments of norms of trajectories given for the slow and fast components of the full order system the estimation of the rate of convergence of the full order system is also shown

an improved l2 decay for weak solutions of a boussinesq system in exterior domains abstract the algebraic decay for the total kinetic energy of weak solutions of the viscous boussinesq system in an exterior domain is given by means of the spectral analysis method of the stokes operator which gives a positive answer to the l 2 decay question in 11

almost sure exponential stability of recurrent neural networks with markovian switching this paper presents new stability results for recurrent neural networks with markovian switching first algebraic criteria for the almost sure exponential stability of recurrent neural networks with markovian switching and without time delays are derived the results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration next both delay dependent and delay independent criteria for the almost sure exponential stability of recurrent neural networks with time varying delays and markovian switching parameters are derived by means of a generalized stochastic halanay inequality the results herein include existing ones for recurrent neural networks without markovian switching as special cases finally simulation results in three numerical examples are discussed to illustrate the theoretical results

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

new criteria on exponential stability of neutral stochastic differential delay equations neutral stochastic differential delay equations nsddes have recently been studied intensively see e g v b kolmanovskii v r nosov stability and periodic modes of control systems with aftereffect nauka moscow 1981 x mao exponential stability in mean square of neutral stochastic differential functional equations systems control lett 26 1995 245 251 x mao razumikhin type theorems on exponential stability of neutral stochastic functional differential equations siam j math anal 28 2 1997 389 401 x mao stochastic differential equations and their applications horwood publishing chichester 1997 more recently mao asymptotic properties of neutral stochastic differential delay equations stochastics and stochastics rep 68 2000 273 295 provided with some useful criteria on the exponential stability for nsddes however the criteria there require not only the coefficients of the nsddes to obey the linear growth condition but also the time delay to be a constant one of our aims in this paper is to remove these two restrictive conditions moreover the key condition on the diffusion operator associated with the underlying nsdde will take a much more general form our new stability criteria not only cover many highly non linear nsddes with variable time delays but they can also be verified much more easily than the known criteria

asymptotic stability and boundedness of delay switching diffusions multiple lyapunov functions are used to establish sufficient conditions for locating the limit sets of switching diffusions the conditions lead to a number of useful results on stochastic asymptotic stability and boundedness for this class of stochastic hybrid systems

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

interval stability and stabilization of linear stochastic systems this technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time invariant systems first the notion of beta alpha stability of stochastic systems is defined and some relationships among the beta alpha stability the decay rate of system state response and the second order moment lyapunov exponent are revealed we then address the beta alpha stabilization problem and give a sufficient condition via a linear matrix inequality approach

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

stability analysis of stochastic delayed systems with an application to multi agent systems this technical note is concerned with the stability problem of stochastic delayed systems by using a more general halanay type inequality with time varying coefficients a new comparison principle of the proposed halanay type inequality is developed to ensure the stability of stochastic delayed systems the p th moment stability p th moment asymptotic stability and p th moment exponential stability are investigated by means of the proposed general halanay type inequality two examples including one of the consensus of multi agent systems with time varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results

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

pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized h representation abstract the problem of pth moment asymptotic interval stability and stabilization for linear stochastic systems is investigated in this paper firstly we define the generalized h representation which is very helpful to transform stochastic systems into deterministic systems then the problems of pth moment interval stability the decay rate of state response and the estimation of pth moment lyapunov exponent are proposed with the help of the model transformation method furthermore the criteria for pth moment interval stabilization of the linear stochastic systems are addressed some necessary numerical examples are also provided to show the effectiveness of the addressed method

existence regularity and decay rate of solutions of non newtonian flow the existence and the regularity of young measure valued solutions to non newtonian flows are considered furthermore the uniqueness of solutions and their asymptotic behavior are given

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

generalised theory on asymptotic stability and boundedness of stochastic functional differential equations asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations sfdes see e g appleby and reynolds 2008 appleby and rodkina 2009 basin and rodkina 2008 khasminskii 1980 mao 1995 mao 1997 mao 2007 rodkina and basin 2007 shu lam and xu 2009 yang gao lam and shi 2009 yuan and lygeros 2005 and yuan and lygeros 2006 in general the existing results on asymptotic stability and boundedness of sfdes require i the coefficients of the sfdes obey the local lipschitz condition and the linear growth condition ii the diffusion operator of the sfdes acting on a c 2 1 function be bounded by a polynomial with the same order as the c 2 1 function however there are many sfdes which do not obey the linear growth condition moreover for such highly nonlinear sfdes the diffusion operator acting on a c 2 1 function is generally bounded by a polynomial with a higher order than the c 2 1 function hence the existing criteria on stability and boundedness for sfdes are not applicable and we see the necessity to develop new criteria our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up bound for the diffusion operator may take a much more general form

on strong feller recurrence and weak stabilization of regime switching diffusions focusing on two component markov processes having continuous dynamics and discrete events this work develops asymptotic properties of regime switching diffusions first strong feller property is established next classifying the underlying processes as recurrence positive recurrence or null recurrence or transience sufficient conditions for such processes are obtained in addition to providing general criteria for recurrent and transient switching diffusions for processes that are linearizable with respect to the continuous component easily verifiable conditions are established also provided are conditions for null recurrent processes furthermore conditions for controlled switching diffusions in which the feedback controls ensure weak stability or ergodicity are given finally simple examples are used for demonstration

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

almost sure and moment exponential stability in the numerical simulation of stochastic differential equations relatively little is known about the ability of numerical methods for stochastic differential equations sdes to reproduce almost sure and small moment stability here we focus on these stability properties in the limit as the timestep tends to zero our analysis is motivated by an example of an exponentially almost surely stable nonlinear sde for which the euler maruyama em method fails to reproduce this behavior for any nonzero timestep we begin by showing that em correctly reproduces almost sure and small moment exponential stability for sufficiently small timesteps on scalar linear sdes we then generalize our results to multidimensional nonlinear sdes we show that when the sde obeys a linear growth condition em recovers almost surely exponential stability very well under the less restrictive condition that the drift coefficient of the sde obeys a one sided lipschitz condition where em may break down we show that the backward euler method maintains almost surely exponential stability

existence uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay in this paper we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm email protected sup q 0 f q 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 furthermore we give the continuous dependence of solutions on the initial value by means of the corollary of bihari inequality

on delay dependent stability for a class of nonlinear stochastic systems with multiple state delays abstract global asymptotic stability conditions for nonlinear stochastic systems with multiple state delays are obtained based on the convergence theorem for semimartingale inequalities without assuming the lipschitz conditions for nonlinear drift functions the lyapunov krasovskii and degenerate functionals techniques are used the derived stability conditions are directly expressed in terms of the system coefficients nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given

large time decay and growth for solutions of a viscous boussinesq system in this paper we analyze the decay and the growth for large time of weak and strong solutions to the three dimensional viscous boussinesq system we show that generic solutions blow up as t in the sense that the energy and the l norms of the velocity field grow to infinity for large time for 1 p 3 in the case of strong solutions we provide sharp estimates both from above and from below and explicit asymptotic profiles we also show that solutions arising from u0 0 with zero mean for the initial temperature 0 have a special behavior as x or t tends to infinity contrarily to the generic case their energy dissipates to zero for large time

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

on the pth moment exponential stability criteria of neutral stochastic functional differential equations the paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the ito type this investigation can be very complicated even in many special cases by using usual methods based on lyapunov functionals in this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations

stochastic stabilization of differential systems with general decay rate some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general decay rate are first proved then these results are interpreted as suitable stabilization ones for deterministic and stochastic systems also they permit us to construct appropriate linear stabilizers in some particular situations

brief paper noise suppresses explosive solutions of differential systems with coefficients satisfying the polynomial growth condition in this paper we investigate the problem of suppression explosive solutions by noise for nonlinear deterministic differential system given a deterministic differential system email protected t f y t t with coefficients satisfying a more general one sided polynomial growth condition we introduce brownian noise feedback and therefore stochastically perturb this system into the nonlinear stochastic differential system dx t f x t t dt x t email protected t db t we show that appropriate b s guarantee that this stochastic system exists as a unique global solution although the corresponding deterministic systems may explode in a finite time under some weaker conditions we reveal that the single noise x t email protected t db t can also make almost every path of the solution of corresponding stochastically perturbed system grow at most polynomially

on l 1 summability and asymptotic profiles for smooth solutions to navier stokes equations in a 3d exterior domain the exterior nonstationary problem is studied for the 3d navier stokes equations the l1 summability is proved for smooth solutions which correspond to initial data satisfying certain symmetry and moment conditions the result is then applied to show that such solutions decay in time more rapidly than observed in general furthermore an asymptotic expansion is deduced and a lower bound estimate is given for the rates of decay in time

razumikhin type theorems on stability of neutral stochastic functional differential equations recently mao 1995 initiated the study of exponential stability of neutral stochastic functional differential equations nsfdes and employed the razumikhin techniques to investigated the stability problem of nsfdes however the importance of general asymptotic stability has not been considered this paper studies razumikhin type theorems on general pth moment asymptotic stability of nsfdes the theorems established in this paper work for some cases to which the existing results cannot be applied

robust stochastic stabilization and h control of uncertain neutral stochastic time delay systems this paper investigates the problems of robust stochastic stabilization and robust h control for uncertain neutral stochastic time delay systems with time varying norm bounded parameter uncertainties appearing in both the state and input matrices the time delay is assumed to be unknown sufficient conditions for the existence of state feedback controllers are proposed which ensure mean square asymptotic stability of the resulting closed loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties a linear matrix inequality approach is employed to design the desired state feedback controllers furthermore in the case when time delays appear in both the state and control input results on the robust stochastic stabilization and robust h control are also presented an illustrative example is provided to show the potential of the proposed techniques

technical communique a new result on stability analysis for stochastic neutral systems this paper discusses the mean square exponential stability of stochastic linear systems of neutral type applying the lyapunov krasovskii theory a linear matrix inequality based delay dependent stability condition is presented the use of model transformations cross term bounding techniques or additional matrix variables is all avoided thus the method leads to a simple criterion and shows less conservatism the new result is derived based on the generalized finsler lemma gfl gfl reduces to the standard finsler lemma in the absence of stochastic perturbations and it can be used in the analysis and synthesis of stochastic delay systems moreover gfl is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results

on almost sure sample stability of nonlinear stochastic dynamic systems in this note an extension of khasminskii s theorem on almost sure stability of linear stochastic differential equations to a class of nonlinear stochastic differential equations is presented the necessary and sufficient conditions for almost sure stability are proved it is shown that in the second order case the stable region can be exactly determined by studying the singular boundaries of one dimensional diffusion processes the authors present a modified form of feller s criteria for classification of singular boundaries the new criteria are equivalent to and much simpler for applications than feller s criteria two examples of nonlinear stochastic dynamic systems with stable regions illustrate the application procedures

new lyapunov conditions of stochastic finite time stability and instability of nonlinear time varying sdes in this paper we further consider the problem of stochastic finite time stability and instability of nonlinear stochastic differential equations sdes with time varying drift and diffusion terms

new criteria on asymptotic behavior of neutral stochastic functional differential equations this paper investigates the asymptotic behavior of neutral stochastic functional differential equations nsfdes under both the local lipschitz condition and the one dependent on the diffusion operator and on a coercivity term which is more general than the classical growth condition some sufficient conditions for stability with general decay rate and boundedness of nsfdes are derived via the lyapunov analysis method and some stochastic analysis techniques our results not only cover a wide class of highly nonlinear nsfdes but they can also deal with general stability issues including the polynomial stability and the exponential stability finally an illustrative example is provided to show the effectiveness of our theoretical results

the existence and uniqueness of the solution for stochastic functional differential equations with infinite delay abstract 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 r d 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 t 0 t moreover the existence and uniqueness theorem still holds on interval t 0 where t 0 r is an arbitrary real number

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

subelliptic estimates on compact semisimple lie groups abstract in this paper we consider a natural subelliptic structure in semisimple compact and connected lie groups and estimate the constant in the so called subelliptic friedrichs knapp stein inequality which has implications in the regularity theory of p energy minimizers

decay rates for the incompressible navier stokes flows in 3d exterior domains abstract the exterior nonstationary problem is studied for the 3d navier stokes equations for which the associated total net force to the boundary may not vanish the time decay properties of the strong solution including the first and second derivatives are shown in l q and weighted spaces in particular the relation of weighted l 1 summability for smooth solutions is discussed in details between the time decay and the total net force exerted by the fluid to the body the conclusions in this article improve and extend results in h bae b jin asymptotic behavior for the navier stokes equations in 2d exterior domains j funct anal 240 2006 508 529 h bae b jin temporal and spatial decay rates of navier stokes solutions in exterior domains bull korean math soc 44 2007 547 567 and in c he t miyakawa on l 1 summability and asymptotic profiles for smooth solutions to navier stokes equations in a 3d exterior domain math z 245 2003 387 417 c he t miyakawa on weighted norm estimates for nonstationary incompressible navier stokes flows in a 3d exterior domain j differential equations 246 2009 2355 2386 respectively

space time decay of navier stokes flows invariant under rotations we show that the solutions to the non stationary navier stokes equations in open image in new window d 2 3 which are left invariant under the action of discrete subgroups of the orthogonal group o d decay much faster as open image in new window than in generic case and we compute for each subgroup the precise decay rates in space time of the velocity field

on the exponential stability of switching diffusion processes in this note we investigate almost sure exponential stability for a class of switching diffusion processes lyapunov type sufficient conditions to ensure this type of stability for nonlinear switching diffusions are derived the conditions are an improvement over related results in the literature since they do not rely on the moment stability of the system these conditions are then specialized to case of linear switching diffusion processes to provide easily checkable sufficient criteria for exponential stabilization and robust stability

a study of a class of stochastic differential equations with non lipschitzian coefficients we study a class of stochastic differential equations with non lipschitz coefficients a unique strong solution is obtained and the non confluence of the solutions of stochastic differential equations is proved the dependence with respect to the initial values is investigated to obtain a continuous version of solutions the modulus of continuity of coefficients is assumed to be less than x y log open image in new window finally a large deviation principle of freidlin wentzell type is also established in the paper

lower bounds of rates of decay for solutions to the navier stokes equations where a p 3 2 p 1 and the constant c depends on the l2 and lnorms of the initial data u0 this paper deals with the more subtle problem of deriving lower bounds on the energy decay rates we show that for a certain class of initial data the solutions u x t to the 2d and 3d navier stokes equations admit an algebraic lower bound on the energy decay specifically there are two cases to consider in the first case the average of the initial data f u0 dx is nonzero this case was treated in the earlier paper 5 where it was established that

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