a note on the embedding problem for multidimensional fuzzy number spaces this paper generalize the results in wu and zhang fuzzy sets and systems in press the embedding is extended from one dimensional to n dimensional case

the solutions of linear fuzzy stochastic differential systems as a completion of previous work of feng fuzzy sets and systems 115 2000 351 on the general theory of fuzzy stochastic differential systems the solutions of linear fuzzy stochastic differential systems for general coefficient matrix are discussed

rates of clustering for some gaussian self similar processes the analogue of strassen s functional law of the iterated logarithm in known for many gaussian processes which have suitable scaling properties and here we establish rates at which this convergence takes place we provide a new proof of the best upper bound for the convergence tok by suitably normalized brownian motion and then continue with this method to get similar bounds for the brownian sheet and other self similar gaussian processes the previous method which produced these results for brownian motion in 1 was highly dependent on many special properties unavailable when dealing with other gaussian processes

portfolio selection problem with value at risk constraints under non extensive statistical mechanics the optimal portfolio selection problem is a major issue in the financial field in which the process of asset prices is usually modeled by a wiener process that is the return distribution of the asset is normal however several empirical results have shown that the return distribution of the asset has the characteristics of fat tails and aiguilles and is not normal in this work we propose an optimal portfolio selection model with a value at risk var constraint in which the process of asset prices is modeled by the non extensive statistical mechanics instead of the classical wiener process the model can describe the characteristics of fat tails and aiguilles of returns using the dynamic programming principle we derive a hamilton jacobi bellman hjb equation then employing the lagrange multiplier method we obtain closed form solutions for the case of logarithmic utility moreover the empirical results show that the price process can more accurately fit the empirical distribution of returns than the familiar wiener process in addition as the time increases the constraint becomes binding that is to control the risk the agent reduces the proportion of the wealth invested in the risky asset furthermore at the same confidence level the agent reduces the proportion of the wealth invested in the risky asset more quickly under our model than under the model based on the wiener process this can give investors a good decision making reference

pricing a contingent claim with random interval or fuzzy random payoff in one period setting this article proposes a method for pricing a contingent claim with random interval and fuzzy random payoff on introduction of the acceptability concept based on classical no arbitrage argument a price interval and a fuzzy price are obtained in random interval market and fuzzy random market respectively new definitions on replicative strategies sub replicative and sup replicative ones in two market setting are given some interesting results similar to those in the classical random market are presented

sums of independent fuzzy random variables the question when sums of independent fuzzy random variables converge almost surely is discussed in detail similar to the case of real valued random variables the kolmogorov three series theorem is established

levy area of wiener processes in banach spaces the goal of this paper is to construct canonical levy area processes for banach space valued brownian motions via dyadic approximations the significance of the existence of canonical levy area processes is that a stochastic integration theory can be established for such brownian motions in banach spaces existence of flows for stochastic differential equations with infinite dimensional noise then follows via the results of lyons and lyons and qian see e g system control and rough paths 2000 oxford univ press this investigation involves a careful analysis on the choice of tensor norms motivated by the applications to infinite dimensional stochastic differential equations

flow of diffeomorphisms induced by a geometric multiplicative functional in this paper it is shown that the unique multiplicative functional solution to a differential equation driven by a geometric multiplicative functional consitutes a flow of local diffeomorphisms in the case where the driving geometric multiplicative functional is generated by a brownian motion the result in particular presents an answer to an open problem proposed in ikeda and watanabe 4

laplace s method for the laws of heat processes on loop spaces abstract in this paper we will consider laplace s method for a class of heat processes on loop spaces we will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the hessian at the point is non degenerate this kind of process was first introduced by p malliavin in 1990 for the loop group case and then gradually generalized by various authors our tool is the rough path theory of t lyons this technique was pioneered by s aida for finite dimensional processes in his unpublished paper

semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space abstract we study a semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space key results are semiboundedness theorem of the schrodinger operator laplace type asymptotic formula and ims localization formula we also make a remark on the semiclassical problem of a schrodinger operator on a path space over a riemannian manifold

dual method for continuous time markowitz s problems with nonlinear wealth equations continuous time mean variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method a necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique it is also shown that the optimal wealth and portfolio is the solution of a forward backward stochastic differential equation with constraints

stochastic analysis rough path analysis and fractional brownian motions in this paper we show by using dyadic approximations the existence of a geometric rough path associated with a fractional brownian motion with hurst parameter greater than 1 4 using the integral representation of fractional brownian motions we furthermore obtain a skohorod integral representation of the geometric rough path we constructed by the results in ly1 a stochastic integration theory may be established for fractional brownian motions and strong solutions and a wong zakai type limit theorem for stochastic differential equations driven by fractional brownian motions can be deduced accordingly the method can actually be applied to a larger class of gaussian processes with covariance functions satisfying a simple decay condition

on embedding problems of fuzzy number spaces iv in this paper we are going to follow the preceding papers to investigate the embedding problem of fuzzy number space ne 1 by means of a concrete embedding operator using the embedding operator some subclasses of ne 1 and metrices on ne 1 are also investigated

stochastic area for brownian motion on the sierpinski gasket we construct a levy stochastic area for brownian motion on the sierpinski gasket the standard approach via ito integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales we thus provide an example demonstrating the restrictions of the semimartingale framework as a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by brownian motion on the sierpinski gasket

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by analytic extension the d dimensional fractional brownian motion fbm for short b t b 1 t b d t t r with hurst exponent 0 1 is a d dimensional centered self similar gaussian process with covariance e b i s b i t 1 2 i j lsl 2 ltl 2 t s 2 the long standing problem of defining a stochastic integration with respect to fbm and the related problem of solving stochastic differential equations driven by fbm has been addressed successfully by several different methods although in each case with a restriction on the range of either d or the case corresponds to the usual stochastic integration with respect to brownian motion while most computations become singular when gets under various threshhold values due to the growing irregularity of the trajectories as 0 we provide here a new method valid for any d and for 1 4 by constructing an approximation e t e 0 of fbm which allows to define iterated integrals and then applying the geometric rough path theory the approximation relies on the definition of an analytic process z on the cut plane z c r of which fbm appears to be a boundary value and allows to understand very precisely the well known see 5 but as yet a little mysterious divergence of levy s area for 1 4

approximation metric entropy and small ball estimates for gaussian measures a precise link proved by kuelbs and li relates the small ball behavior of a gaussian measure on a banach space e with the metric entropy behavior of k the unit ball of the reproducing kernel hilbert space of in e we remove the main regularity assumption imposed on the unknown function in the link this enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates for concrete gaussian processes moreover we show that the small ball behavior of a gaussian process is also tightly connected with the speed of approximation by finite rank processes

global existence and uniqueness of solutions for fuzzy differential equations under dissipative type conditions in this paper using the properties of a differential and integral calculus for fuzzy set valued mappings and completeness of metric space of fuzzy numbers the global existence uniqueness and the continuous dependence of a solution on a fuzzy differential equation are derived under the dissipative type conditions we also present the global existence and uniqueness of solutions for a fuzzy differential equation on a closed convex subset of fuzzy number space

existence and uniqueness of cauchy problem for fuzzy differential equations under dissipative conditions the existence theorem of peano for the fuzzy differential equation x t f t x t x t 0 x 0 does not hold in general except in the special case where the fuzzy number space e n d is finite dimensional 1 or f is assumed to be continuous and bounded 2 in this paper the dissipative type conditions which guarantee the existence theorem for peano are specified based on the existence theorem of approximate solutions to above cauchy problem

an embedding theorem for convex fuzzy sets in this paper we embed the space of upper semicontinuous convex fuzzy sets on a banach space into a space of continuous functions on a compact space the following structures are preserved by the embedding convex cone metric sup semilattice the indicator function of the unit ball is mapped to the constant function 1 two applications are presented strong laws of large numbers for fuzzy random variables and korovkin type approximation theorems

rough paths analysis of general banach space valued wiener processes abstract in this article we carry out a rough paths analysis for banach space valued wiener processes we show that most of the features of the classical wiener process pertain to its rough path analog to be more precise the enhanced process has the same scaling properties and it satisfies a fernique type theorem a support theorem and a large deviation principle in the same holder topologies as the classical wiener process does moreover the canonical rough paths of finite dimensional approximating wiener processes converge to the enhanced wiener process finally a new criterion for the existence of the enhanced wiener process is provided which is based on compact embeddings this criterion is particularly handy when analyzing kunita flows by means of rough paths analysis which is the topic of a forthcoming article

a convergence theorem of fuzzy valued martingales in the extended hausdorff metric h in this paper we shall give a new embedding method to prove a convergence theorem for fuzzy valued random variables in the sense of the extended hausdorff metric h without the restriction of fuzzy sets satisfying the lipschitz condition

precise asymptotics of certain wiener functionals abstract in this article we present a method for developing certain wiener integrals in an asymptotic expansion as the variance of the wiener goes to 0 the basic ideas are a combination of methods borrowed from the theory of large deviations together with techniques from the calculus of wiener space

asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths abstract in this paper we establish asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths under the condition that the phase function has finitely many non degenerate minima our main tool is the banach space valued rough path theory of t lyons we use a large deviation principle and the stochastic taylor expansion with respect to the topology of the space of geometric rough paths this is a continuation of a series of papers by inahama y inahama laplace s method for the laws of heat processes on loop spaces j funct anal 232 2006 148 194 and by inahama and kawabi y inahama h kawabi large deviations for heat kernel measures on loop spaces via rough paths j london math soc 73 3 2006 797 816 y inahama h kawabi on asymptotics of certain banach space valued ito functionals of brownian rough paths in proceedings of the abel symposium 2005 stochastic analysis and applications a symposium in honor of kiyosi ito springer berlin in press available at http www abelprisen no no abelprisen deltagere 2005 html

the levy area process for the free brownian motion abstract in this paper we construct a levy area process for the free brownian motion and in this way a typical geometric rough path in the sense of t lyons 1998 rev mat iberoamer 14 215 310 lying above the free brownian path thus the general results of lyons on differential equations driven by rough paths may be applied to the free brownian motion case

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

portfolio selection problem with nonlinear wealth equations under non extensive statistical mechanics for time varying sde abstract this paper is dedicated to the study of continuous time mean variance optimal portfolio selection problem with non linear wealth equations under non extensive statistical mechanics for the time varying stochastic differential equation model firstly we allow the returns and variance of risky assets are time varying functions which can fit the financial data better secondly we consider an investor with the non linear wealth equation in fact the wealth equations are not linear in many cases the investor has to pay some taxes which leads to a non linear wealth equation moreover since the return of the stocks price may be affected by a large investors portfolio selection the wealth equation is non linear in this case thirdly the non linear wealth equation driven by tsallis distribution is constructed under non extensive statistical mechanics which can capture the characteristics of fat tails and aiguilles of the risky asset s return the viscosity solution of the hjb equation for the portfolio problem is proposed by the optimal stochastic control theory and lagrange multiplier method finally the efficient portfolio strategy and efficient frontier under non extensive statistical mechanics are obtained furthermore numerical analysis and real data study are discussed to show our results