theory of markov systems with fuzzy states in this paper the theory of fuzzy logic is combined with the theory of markov systems and the concept of a markov system with fuzzy states is introduced for the first time the main objective is to develop a methodology of describing a markov population system with fuzzy states this is an effort to deal with the fact that in real applications one is often faced with fuzzy states this paper investigates the properties of a markov system with states that have imprecise boundaries a full description of a nonhomogeneous markov system with fuzzy states is outlined and the basic parameters of the system are provided more specifically the expected population structure of the system is found and given in a closed analytic form and the asymptotic behaviour of the system is provided under the more realistic assumption of a fuzzy set space

fuzzy markovian decision process in this paper a markovian decision process with fuzzy states is considered it is shown that if the markov chain associated with the process of non fuzzy states is irreducible then the corresponding markov chain associated with the fuzzy states is also irreducible the importance of this result lies in the fact that the traditional methods for solving the markovian decision process can be used in the case with fuzzy states also

corrigendum to mixed interpolating smoothing splines and the v spline j math anal appl 322 2006 28 40 abstract in 6 the problem of mixed interpolation and smoothing by splines was generalized and applied to certain practical problems in particular conditions for the existence of solutions were provided in theorem 1 in proposition 6 of 8 it was shown that solutions may not always exist under the conditions of theorem 1 therefore it is the purpose of this paper to rectify this theorem we do so with an additional condition on finiteness of the kernel of an operator while the original proof holds with this finiteness assumption we provide a revised proof that more clearly shows where this assumption is used this extra assumption of finiteness has been assumed in all examples by the author in 6

infinite products of matrices with some negative elements and row sums equal to one abstract infinite products of a class of matrices the v matrices with some negative elements and row sums equal to one are studied after a series of lemmas and propositions a basic theorem is provided where it is shown that the limit of an infinite product of v matrices under certain conditions exists finally a method for finding this limit based on some properties of generalized inverses is provided

de rham hodge kodaira operator on loop groups we consider a based loop group le g over a compact lie groupg endowed with its pinned wiener measure the law of the brownian bridge ong and we shall calculate the ricci curvature for differentialn forms over le g a type of bochner weitzenbock formula for general differentialn forms or shigekawa identity will be established

the perturbed nonhomogeneous markov system abstract in this paper we introduce for the first time the concept of a perturbed nonhomogeneous markov system p nhms the expected population structure is found and its asymptotic behavior is provided under more realistic assumptions than previous studies by relaxing the assumption that the imbedded nonhomogeneous markov chain of a nhms is converging to a homogeneous markov chain also we study the sensitivity of the limiting expected structure on perturbations of the limiting input probabilities for a nhms moreover the asymptotic behavior of the variances and covariances of the class sizes of a p nhms is considered and found in an elegant closed analytic form

modulus of continuity of the canonic brownian motion on the group of diffeomorphisms of the circle abstract an explicit modulus of holder continuity is given for the flow associated to the canonic brownian motion on the diffeomorphism group of the circle

brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2d stochastic euler equation abstract a geometric brownian motion performs a continuous time infinitesimal perturbation of the state of the system this perturbation conserves the energy exact expression for the energy transfer towards high modes is obtained ensuring existence for all time of the solution

asymptotic behaviour of the survival probabilities in an inhomogeneous semi markov model for the migration process in credit risk abstract we start with the stochastic foundation of the general discrete time market of defaultable bonds we prove that the above market is viable if and only if there exists an equivalent martingale measure from which we construct the forward probability measure and under which the discounted default free bond price is a martingale assuming that the migration process of defaultable bonds evolves as an inhomogeneous semi markov process we study the asymptotic behaviour of survival probabilities we provide a method of estimating real world transition probability sequences for the semi markov process and statistics for testing their homogeneity over time

periodicity of infinite products of matrices with some negative elements and row sums equal to one abstract the problem of periodicity for the infinite products of a class of matrices the v matrices with some negative elements and row sums equal to one is studied after a series of lemmas propositions and theorems a basic theorem is proved that an infinite product of v matrices under certain conditions splits into a number of subsequences which converge geometrically fast finally a method for finding these limits based on some properties of generalized inverses is provided

nonstationary cyclic behavior in markov systems abstract we introduce the concept of the nonstationary cyclic markov system as a natural extension of the cyclic systems found in recent literature we find the sets of d cyclic asymptotically attainable structures and establish the relationships that exist between these structures for a nonhomogeneous markov system in a deterministic or stochastic environment the inherent connection between nonstationary cyclicity and stochastic environment is examined also we investigate the conditions under which there exists a geometric convergence to the equilibrium

rate of convergence asymptotically attainable structures and sensitivity in non homogeneous markov systems with fuzzy states this paper is concerned with the rate of convergence the asymptotically attainable structures and the sensitivity of a non homogeneous markov system nhms in short with fuzzy states more specifically it is proved that under some realistic assumptions easily met in practice the convergence rate of the relative population structure to its limit is geometric furthermore the asymptotically attainable structures in a nhms with fuzzy states are given more precisely the problem of finding which states are possible as limiting ones in a nhms with fuzzy states is studied provided that the limit of the sequence of the input probability vectors is controlled moreover the sensitivity of the limiting expected population structure on perturbations of the limiting input probabilities for the system is also studied two applications in cognitive science and in manpower planning are given where the sensitivity of two nhms with three states is studied provided that the limiting input probability vector is perturbed

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

on the spatial asymptotic behavior of stochastic flows in euclidean space we study asymptotic growth rates of stochastic flows on r d and their derivatives with respect to the spatial parameter under lipschitz conditions on the local characteristics of the generating semimartingales in a first step these conditions are seen to imply moment inequalities for the flow of the form e sup 0t x 0t y p 1 0 t t in a second step we deduce the growth rates from an integrated version of these moment inequalities using the continuity lemma of garsia rodemich and rumsey we provide two examples to show that our results are sharp

periodicity of asymptotically attainable structures in nonhomogeneous markov systems we find the sets of d periodic asymptotically attainable structures and we establish the periodicities that exist between these structures for a nonhomogeneous markov system in the case where the imbedded nonhomogeneous markov chain is periodic with period d also it is proved that under certain conditions each converging subsequence of the sequence of relative structures has a geometric rate of convergence

asymptotic variability of nonhomogeneous markov systems under cyclic behaviour abstract in this paper the asymptotic variability of nonhomogeneous markov systems under cyclic behaviour is studied it is found that the sequence of vectors of means variances and covariances splits into d subsequences which converge where d is the period of the cyclic finally an illustration of the present results with data from a manpower system is given

on isotropic brownian motions this paper includes a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropic gaussian fields characteristic exponents stability asymptotic behaviour statistical equilibrium are the topics on which the main results are obtained

nonergodicity of euler fluid dynamics on tori versus positivity of the arnold ricci tensor abstract brownian motions above the group g of volume preserving diffeomorphisms of the torus t d d 2 are constructed the asymptotic behaviour for large time of those processes shows the nonexistence of a probability measure invariant under the deterministic incompressible fluid dynamics the energy induces on the group of volume preserving diffeomorphisms of t 2 a riemannian structure which has a positive renormalized ricci tensor

evolution of a time dependent markov model for training and recruitment decisions in manpower planning the current paper deals with the asymptotic behavior of a generalized time dependent markov manpower planning model this model on the one hand takes into account the need of the employees for eternal training and on the other hand its workforce demand at each time period is satisfied through internal mobility and two streams of recruitment the first originating from the outside environment and the second from a supplementary auxiliary system for the model under discussion we provide two sets of conditions concerning the existence and the specification of its expected limiting structure a numerical application illustrating the present results in a typical manpower system follows

on a problem in population structure abstract the paper deals with a markov process that describes the age distribution in a population the limit distribution is well known we are here concerned with the speed of convergence second largest eigenvalue the exposition is independent of the theory of nonnegative matrices

flows coalescence and noise we are interested in stationary fluid random evolutions with independent increments under some mild assumptions we show they are solutions of a stochastic differential equation sde there are situations where these evolutions are not described by flows of diffeomorphisms but by coalescing flows or by flows of probability kernels in an intermediate phase for which there exist a coalescing flow and a flow of kernels solution of the sde a classification is given all solutions of the sde can be obtained by filtering a coalescing motion with respect to a subnoise containing the gaussian part of its noise thus the coalescing motion cannot be described by a white noise

mixed interpolating smoothing splines and the v spline abstract in their monograph bezhaev and vasilenko have characterized the mixed interpolating smoothing spline in the abstract setting of a hilbert space in this paper we derive a similar characterization under slightly more general conditions this is specialized to the finite dimensional case and applied to a few well known problems including the spline a piecewise polynomial spline in tension and near interpolation as well as interpolation and smoothing in particular one of the main objectives in this paper is to show that the spline is actually a mixed spline an observation that we believe was not known prior to this work we also show that the spline is a limiting case of smoothing splines as certain weights increase to infinity and a limiting case of near interpolants as certain tolerances decrease to zero we conclude with an iteration used to construct curvature bounded spline curves

asymptotically attainable structures in nonhomogeneous markov systems in this paper we provide and study a new aspect in the classical problem of the asymptotic behavior of a nonhomogeneous markov system nhms the set of asymptotically attainable structures is determined as the convex hull of k vertices which are given also the rate of convergence to asymptotically attainable structures is studied and conditions are provided for the convergence to be geometrically fast finally an illustration of the results with data from manpower systems is provided

on the problems of smoothing and near interpolation in the first part of this paper we apply a saddle point theorem from convex analysis to show that various constrained minimization problems are equivalent to the problem of smoothing by spline functions in particular we show that near interpolants are smoothing splines with weights that arise as lagrange multipliers corresponding to the constraints in the problem of near interpolation in the second part of this paper we apply certain fixed point iterations to compute these weights a similar iteration is applied to the computation of the smoothing parameter in the problem of smoothing

best near interpolation by curves existence the conditions derived in k scherer and p w smith siam j numer anal 20 1989 pp 160 168 for the existence of minimizers to the nonlinear problem of best interpolation by curves are extended to the problem of best near interpolation by curves that meet arbitrary sets such as closed balls as in s kersey best near interpolation by curves optimality conditions technical report 99 05 center for the mathematical sciences university of wisconsin madison wi 1999 the minimizers are spline curves with breakpoints at the data sites at which the curves meet the sets and the nonlinearities arise as these data sites vary from curve to curve the results here apply to hermite type interpolation conditions with the possibility of repeated data sites

transfer of stochastic energy towards high modes and its application to diffeomorphism flows on tori abstract dissipativity towards high modes is a classical question in hydrodynamics for some stochastic model this dissipativity can be exactly computed through the asymptotic of a jump process on the modes this asymptotical study is the object of this paper

on euler trapezoid formulae modified versions of the euler trapezoid formula for functions whose derivatives are either functions of bounded variation or lipschitzian functions or functions in l p spaces are given the results are applied to quadrature formulae