razumikhin type theorems on general decay stability of stochastic functional differential equations with infinite delay to the best of the authors knowledge there are no results based on the so called razumikhin technique via a general decay stability for any type of stochastic differential equations in the present paper the razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay the obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given an example is presented to illustrate the usefulness of the theory

moment estimate and existence for solutions of stochastic functional differential equations abstract in this paper we give the existence uniqueness theorems and the moment estimates of solutions for a large class of sfdes these estimates improve and extend some related results including exponential stability decay stability and asymptotic behavior their corollaries improve and extend the classical halanay inequality and some of its generalizations moreover the stochastic version of the wintner theorem in continuous function space is established by the compare principle which improves and extends the main results of xu et al 2008 2013 when the methods presented are applied to the sfdes with impulses and sfdes in hilbert spaces we extend the related results of govindan and ahmed 2013 liu et al 2007 2010 vinodkumar 2010 and xu et al 2012 two examples are provided to illustrate the effectiveness of our results

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

systems of frequency distributions for water and environmental engineering abstract a wide spectrum of frequency distributions are used in hydrologic hydraulic environmental and water resources engineering these distributions may have different origins are based on different hypotheses and belong to different generating systems review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include 1 differential equations 2 distribution elasticity 3 genetic theory 4 generating functions 5 transformations 6 bessel function 7 expansions and 8 entropy maximization this paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems it also proposes based on empirical evidence another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering

remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay in this paper we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm f 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

the stability with general decay rate of neutral stochastic functional hybrid differential equations with levy noise abstract this paper is concerned with the existence and uniqueness the almost sure stability with general decay rate including almost sure exponential stability almost sure polynomial stability and almost sure logarithmic stability for the global solution of nonlinear neutral stochastic functional hybrid differential equations with levy noise the key technique used is the method of lyapunov function nonnegative semi martingale convergence theorem and the theory of m matrix we use auxiliary functions to dominate the corresponding lyapunov function and the diffusion operator our conditions on the diffusion operator are weaker than those in the related existing works finally one example is given to show the effectiveness of the obtained theory

a strategy of problem solving in a fuzzy reasoning network this paper deals with the development of a strategy of problem solving in a fuzzy reasoning network the propositions involved are temporal knowledge representation with hierarchical or network structure in a fuzzy sense and forward and backward fuzzy reasoning the strategies as developed might be applicable to various fuzzy reasoning problems existing in the real world

razumikhin method and exponential stability of hybrid stochastic delay interval systems this paper deals with the exponential stability of hybrid stochastic delay interval systems also known as stochastic delay interval systems with markovian switching the known results in this area see e g x mao exponential stability of stochastic delay interval systems with markovian switching ieee trans automat control 47 10 2002 1604 1612 require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics the main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only the razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay

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

a new approach of multi stage fuzzy logic inference abstract in general multi stage fuzzy logic inference there are three kinds of linguistic variables input output and intermediate variables when intermediate variables are present in a set of fuzzy rules to form multi stage fuzzy rules the inferring time involved is understandably lengthened to achieve fast reasoning of multi stage fuzzy logic the number of fuzzy set operations of input output and intermediate variables must be decreased as much as possible without information loss for the intermediate variables the fuzzy logic operations of overlapped fuzzy value pairs on several multi stage fuzzy rules may be pre computed at compiling time furthermore if the pre computations have been done the numbers of intersection and union scalar operations must also decrease in order to speed up reasoning at execution time moreover whether fuzzy logic operations of multi stage fuzzy rules are pre computed or not the types of fuzzy logic operators must be considered failing to do so may lead to information error by using the truck trailer backer parking system improvements over related methods are attained

a note on stability of hybrid stochastic differential equations the method is different from those usual methods used in previous literature some harsh restrictions imposed on diffusion operators have been removed the differentiability of delays has been removed we studied the robustness of exponential stability respect to delays in this paper the pth moment stability of hybrid stochastic differential equations is investigated several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison principle the proposed criteria remove some harsh restrictions imposed on the diffusion operators and improve some previous related works numerical examples and simulations are given to illustrate the effectiveness of theoretical results

razumikhin type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations abstract in this paper we establish two different th moment type stability criterions on the exact and numerical solutions of the stochastic pantograph differential equations one is established by the virtue of lyapunov method and the other is used by the continuous and discrete razumikhin technique by comparing the two stability criterions we can easily see that the conditions constructed by the razumikhin type technique are better than those constructed by the virtue of lyapunov method using the conditions constructed for the th moment type stability we study the stability of the euler maruyama method and the backward euler maruyama method respectively for a special class of the stochastic pantograph differential equations finally examples are given to illustrate the consistence with the theoretical results on the th moment type stability

razumikhin type exponential stability criteria of neutral stochastic functional differential equations 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 technique the main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with lyapunov functionals the analysis is based on paper x mao razumikhin type theorems on exponential stability of neutral stochastic functional differential equations siam j math anal 28 2 1997 389 401 referring to mean square and almost sure exponential stability

stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks in this paper we investigate the stochastic functional differential equations with infinite delay some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using razumikhin method and lyapunov functions based on the obtained results we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays the result extends and improves the earlier publications two examples are given to illustrate the applicability of the obtained results

on the generalized cumulative residual entropy with applications in actuarial science recently psarrakos and navarro 2013 proposed a new measure of uncertainty which extends the cumulative residual entropy cre called the generalized cumulative residual entropy gcre in the present paper new properties and applications in actuarial risk measures of the gcre are explored bounds stochastic order properties and characterization results of the new entropy are also discussed it is shown that the gcre is invariant under changes in location and scale directly with scale of a random variable the same properties also hold for the standard deviation it is also proved that the gcre of the first order statistics can uniquely determine the parent distribution the weibull distribution which is commonly used in several fields of applied probability is characterized by using the mentioned generalized measure the gcre is studied as a risk measure and is compared to the standard deviation and the right tail risk measure where the latter measure was introduced by wang 1998 several examples are also given to illustrate the new results

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

on some stability problems of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract this paper covers the topic of both the p th moment p 2 and almost sure stability of impulsive stochastic cohen grossberg neural networks with mixed time delays we partially use a known result on exponential stability of impulsive stochastic functional differential systems based on the razumikhin type technique and extend it to the case of stochastic neural networks using the lyapunov function method and a gronwall type inequality additionally we consider the stability with respect to a general decay function which includes exponential but also more general lower rate decay functions as the polynomial and the logarithmic ones this fact gives us the opportunity to study general decay almost sure stability even when the exponential one cannot be discussed suitable examples which support the theory are also presented

representation and use of imprecise temporal knowledge in dynamic systems abstract in this paper the importance of representation and use of imprecise temporal knowledge for problem solving in industrial dynamic systems is emphasized first a representation of imprecise temporal knowledge is then given for describing the dynamic behavior of systems a novel problem on on line temporal matching and numeric matching is presented and a method for solving this problem is proposed a method for fuzzy proposition reasoning and temporal reasoning is put forward finally as two application examples the fault diagnosis of a fluidized catalytic cracking unit is taken up to illustrate the usefulness of the proposed knowledge representation and methods

on a general decay stability of stochastic cohen grossberg neural networks with time varying delays abstract to the best of our knowledge there are only few results on general decay stability applied to stochastic neural networks for stochastic cohen grossberg neural networks with time varying delays we study in the present paper both the pth moment p 2 and almost sure stability on a general decay rate and partly generalize and improve some known results referring to the exponential stability we also extend the usual notion on a general decay function which allows us to study both the pth moment and almost sure stability even if the exponential stability cannot be shown some examples are presented to support and illustrate the theory

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

stochastic functional differential equations with infinite delay abstract the stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay the main aim of this paper is to close this gap we establish criteria of pth moment t bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay and we also illustrate the result with an example

on the estimation of long tailed skewed distributions with actuarial applications abstract very long tailed skewed distributions often arise in practice in particular we find that size of loss distributions in casualty insurance are mainly of this type compounding explains why many of these losses have approximate pareto generalized pareto burr and log t distributions an adaptation of the empirical mean residual life function helps the statistician select the correct model to fit in these cases it is then discovered that minimum distance estimates in particular that of cramer von mises and minimum chi square estimates are extremely valuable and easy to use in the case of grouped data two substantial examples are given one involving hurricane losses and the other dealing with malpractice claims