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

exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps abstract in this work we investigate stochastic partial differential equations with variable delays and jumps we derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions and generalize the results obtained by taniguchi t taniguchi the exponential stability for stochastic delay partial differential equations j math anal appl 331 2007 191 205 and wan and duan l wan j duan exponential stability of non autonomous stochastic partial differential equations with finite memory statist probab lett 78 5 2008 490 498 to cover a class of more general stochastic partial differential equations with jumps finally an illustrative example is established to demonstrate our established theory

nearly optimal state feedback controls for stochastic systems with wideband noise disturbances much of optimal stochastic control theory is concerned with diffusion models such models are often only idealizations or limits in an appropriate sense of the actual physical process which might be driven by a wide bandwidth not white process or be a discrete parameter system with correlated driving noises optimal or nearly optimal controls derived for the diffusion models would not normally be useful or even of much interest if they were not also nearly optimal for the physical system which the diffusion approximates under quite broad conditions the nearly optimal control for the physical process do have this robustness property even when compared to controls which can depend on all the past driving noise we treat the problem over a finite time interval as well as the average cost per unit time problem weak convergence methods provide the appropriate analytical tools

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

asymptotic optimality theory for decentralized sequential hypothesis testing in sensor networks the decentralized sequential hypothesis testing problem is studied in sensor networks where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the scenario where the sensors have full access to their past observations the first asymptotically bayes sequential test is developed having the same asymptotic performance as the optimal centralized test that has access to all sensor observations next in the scenario where the sensors do not have full access to their past observations a simple but asymptotically bayes sequential tests is developed in which sensor message functions are what we call tandem quantizer where each sensor only uses two different sensor quantizers with at most one switch between these two possibilities moreover a new minimax formulation of optimal stationary sensor quantizers is proposed and is studied in detail in the case of additive gaussian sensor noise finally our results show that in the simplest models feedback from the fusion center does not improve asymptotic performance in the scenario with full local memory however even a one shot one bit feedback can significantly improve performance in the case of limited local memory

bayesian sequential change diagnosis sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence in this problem the common probability law of a sequence of i i d random variables suddenly changes at some disorder time to one of finitely many alternatives this disorder time marks the start of a new regime whose fingerprint is the new law of observations both the disorder time and the identity of the new regime are unknown and unobservable the objective is to detect the regime change as soon as possible and at the same time to determine its identity as accurately as possible prompt and correct diagnosis is crucial for quick execution of the most appropriate measures in response to the new regime as in fault detection and isolation in industrial processes and target detection and identification in national defense the problem is formulated in a bayesian framework an optimal sequential decision strategy is found and an accurate numerical scheme is described for its implementation geometrical properties of the optimal strategy are illustrated via numerical examples the traditional problems of bayesian change detection and bayesian sequential multi hypothesis testing are solved as special cases in addition a solution is obtained for the problem of detection and identification of component failure s in a system with suspended animation

on asian option pricing for nig levy processes in this paper we derive approximations and bounds for the esscher price of european style arithmetic and geometric average options the asset price process is assumed to be of exponential levy type with normal inverse gaussian nig distributed log returns numerical illustrations of the accuracy of these bounds as well as approximations and comparisons of the nig average option prices with the corresponding black scholes prices are given

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 exponential behaviour and stabilizability of stochastic 2d navier stokes equations abstract some results on the pathwise exponential stability of the weak solutions to a stochastic 2d navier stokes equation are established the first ones are proved as a consequence of the exponential mean square stability of the solutions however some of them are improved by avoiding the previous mean square stability in some more particular and restrictive situations also some results and comments concerning the stabilizability and stabilization of these equations are stated

stochastic functional partial differential equations existence uniqueness and asymptotic decay property existence and uniqueness of strong solutions for a class of stochastic functional differential equations in hilbert spaces are established sufficient conditions which guarantee the transference of mean square and pathwise exponential stability from stochastic partial differential equations to stochastic functional partial differential equations are studied the stability results derived are also applied to stochastic ordinary differential equations with hereditary characteristics in particular as a direct consequence our main results improve some of those by mao shah in which it was proved that under certain conditions pathwise exponential stability is transferred from non delay equations to delay equations if the constant time lag appearing in the problem is sufficiently small while in our treatment the transference actually holds for arbitrary bounded delay variables not only in finite but in infinite dimensions

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

interval state estimation for uncertain polytopic systems the aim of this article is the state estimation of uncertain polytopic dynamic systems the parametric uncertainties affecting the system are time varying unknown and bounded with known bounds the objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties this set will be characterized by the lower and upper bounds of the state trajectory given the uncertainty bounds the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a luenberger type observer fed with the system measurements the proposed observer is designed to minimize the interval width of the estimates the observer gains are obtained by solving an optimization problem under lmi constraints the efficiency of the proposed approach is illustrated by numerical examples

stability of stochastic interval systems with time delays abstract consider a given exponentially stable system undergoing a random perturbation which is dependent on a past state of the solution of the system suppose this stochastically perturbed system is described by a stochastic differential functional equation in this paper we establish a sufficient condition that the perturbed system remains exponentially stable using a specific example we show how this condition may be used and we extend it to deal with multiple time delays

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

existence uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in hilbert spaces abstract in this paper we shall consider the existence uniqueness and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r 0 dx t ax t f t x t dt g t x t dw t where we assume that a is a closed densely defined linear operator and the generator of a certain analytic semigroup f c h g c l 0 2 k h are two locally lipschitz continuous functions where c c r 0 d a l 0 2 k h are two proper infinite dimensional spaces 0 w t is a given k valued wiener process and both h and k are separable hilbert spaces

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

reward rate maximization in sequential identification under a stochastic deadline any intelligent system performing evidence based decision making under time pressure must negotiate a speed accuracy trade off in computer science and engineering this is typically modeled as minimizing a bayes risk functional that is a linear combination of expected decision delay and expected terminal decision loss in neuroscience and psychology however it is often modeled as maximizing the long term reward rate or the ratio of expected terminal reward and expected decision delay the two approaches have opposing advantages and disadvantages while bayes risk minimization can be solved with powerful dynamic programming techniques unlike reward rate maximization it also requires the explicit specification of the relative costs of decision delay and error which is obviated by reward rate maximization here we demonstrate that for a large class of sequential multihypothesis identification problems under a stochastic deadline the reward rate maximization is equivalent to a special case of bayes r

recombined multinomial tree based on saddle point approximation and its application to levy models options pricing abstract this paper studies the constructing methods of a recombined multinomial tree based on saddle point approximation and its application to levy models options pricing firstly the levy process and the european option pricing are introduced then we used the characteristic function of levy process to generate density function value at discrete point in a certain range based on the saddle point approximation method then we provide the method to construct recombined multinomial tree and give the pricing formula of european option and path dependent option pricing based on the backward iteration finally we used the cgmy process to demonstrate its application to european option american option and american barrier option pricing it proves that saddle point approximation turns the inverse fourier integral transform problem to several function value calculation comparing to ifft the speed of calculation using this method is faster and it avoid the negative probability density function value based on ifft because of the linear growth of the number of nodes we can extend the saddle point approximation method to the calculation of path dependent option

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

multihypothesis sequential probability ratio tests ii accurate asymptotic expansions for the expected sample size for pt i see ibid vol 45 p 2448 61 1999 we proved in pt i that two specific constructions of multihypothesis sequential tests which we refer to as multihypothesis sequential probability ratio tests msprts are asymptotically optimal as the decision risks or error probabilities go to zero the msprts asymptotically minimize not only the expected sample size but also any positive moment of the stopping time distribution under very general statistical models for the observations in this paper based on nonlinear renewal theory we find accurate asymptotic approximations up to a vanishing term for the expected sample size that take into account the overshoot over the boundaries of decision statistics the approximations are derived for the scenario where the hypotheses are simple the observations are independent and identically distributed i i d according to one of the underlying distributions and the decision risks go to zero simulation results for practical examples show that these approximations are fairly accurate not only for large but also for moderate sample sizes the asymptotic results given here complete the analysis initiated by baum and veeravalli 1994 where first order asymptotics were obtained for the expected sample size under a specific restriction on the kullback leibler distances between the hypotheses

exponential stabilization of stochastic interval system with time dependent parameters abstract there has been growing interest in analyzing stability in design controls of stochastic systems this interest arises out of the need to develop robust control strategies for systems with uncertain dynamics this paper is concerned with the examination of conditions under which the desired structure of a stochastic interval system with time dependent parameters is stabilizable necessary and sufficient condition under which two level preconditioner guarantees quadratic mean exponential stability of the desired structure of uncontrolled stochastic interval system is presented sufficient condition for exponential stability of the equilibrium solution of uncontrolled stochastic interval system is also presented

default prediction with the merton type structural model based on the nig levy process merton s model merton 1974 has long been a standard for estimating company s probability of default pd for listed companies the major advantage of merton s model is the use of current market prices to determine the probability of default the logic behind the model is simple the market prices best reflect all the relevant information being forward looking estimates of company s prospect and should be and are superior to the balance sheet disclosures which at best are ex post realisations of company s performance it is thus a pity that the benefits strengths of merton s model are hindered by a significant shortcoming of the model namely the assumption of normally distributed returns as numerous authors point out barndorff nielsen 1997 5 6 prause 1999 eberlein 2001 brambilla et al 2015 stock returns are not normally distributed which significantly limits the use of model in practice moreover the estimates of pds can be biased downwards exposing the banks to the possibility of undercapitalisation and systematic shocks it is the purpose of this paper to remedy this situation firstly we extend the merton model by allowing for normal inverse gaussian nig distributed returns as several authors point out using the examples of options schoutens 2009 nig in most cases provides a robust statistical platform for estimating stock returns we further extend our approach by constructing a robust em algorithm for estimating pds within the merton nig framework we also test the reliability of the nig improved merton model against classical merton s model for estimating pds applying our results to ljubljana stock exchange we find that the pd estimates using classical merton s model are biased whereas the estimates from nig merton s model are robust

necessary and sufficient conditions for the hurwitz and schur stability of interval matrices establishes a set of new sufficient conditions for the hurwitz and schur stability of interval matrices the authors use these results to establish necessary and sufficient conditions for the hurwitz and schur stability of interval matrices the authors relate the above results to the existence of quadratic lyapunov functions for linear time invariant systems with interval valued coefficient matrices using the above results the authors develop an algorithm to determine the hurwitz and the schur stability properties of interval matrices the authors demonstrate the applicability of their results by means of two specific examples

multihypothesis sequential probability ratio tests i asymptotic optimality the problem of sequential testing of multiple hypotheses is considered and two candidate sequential test procedures are studied both tests are multihypothesis versions of the binary sequential probability ratio test sprt and are referred to as msprts the first test is motivated by bayesian optimality arguments while the second corresponds to a generalized likelihood ratio test it is shown that both msprts are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution when the error probabilities or more generally risks associated with incorrect decisions are small the results are first derived for the discrete time case of independent and identically distributed i i d observations and simple hypotheses they are then extended to general possibly continuous time statistical models that may include correlated and nonhomogeneous observation processes it also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters where the composite hypotheses due to nuisance parameters can be reduced to simple ones by using the principle of invariance these results provide a complete generalization of the results given by veeravalli and baum see ibid vol 41 p 1994 97 1995 where it was shown that the quasi bayesian msprt is asymptotically efficient with respect to the expected sample size for i i d observations

stabilization in probability and mean square of controlled stochastic dynamical system with state delay abstract although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies so far there are few works on controlled stochastic dynamical systems with state delay in this paper a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered condition under which the system is exponentially stable in mean square and in probability is examined