on the geometry of the term structure of interest rates we present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates this includes an extension of the frobenius theorem for fr echet spaces in particular this approach puts new light on many of the classical models such as the hull white extended vasicek and cox ingersoll ross short rate models the notion of a finite dimensional realization fdr is central for this analysis we motivate it classify all generic fdrs and provide some new results for the corresponding factor processes such as hypoellipticity of its generators and the existence of smooth densities furthermore we include finite dimensional external factors thus admitting a stochastic volatility structure

risk sensitive and robust escape criteria the problem of controlling a noisy process so as to prevent it from leaving a prescribed set has a number of interesting applications in this paper new approaches to this problem are considered first a risk sensitive criterion for a stochastic diffusion process model is examined and it is shown that the value is a classical solution of a related pde the qualitative properties of this criterion are favorably contrasted with those of existing criteria in the risk averse limit it is proved that in the risk averse limit the value of the risk sensitive criterion converges to a viscosity solution of a first order pde it is then demonstrated that the value function of a deterministic differential game is also a viscosity solution to the pde this game gives a robust control formulation of the escape time problem and is analogous to h infty control in particular the opposing player attempts to push the process out of the prescribed set and suffers an l2 cost for his efforts lower bounds on the escape time as a function of this cost are obtained

the poisson s loss factor of solid viscoelastic materials the complex poisson s ratio plays an important role in characterizing the linear dynamic behaviour of solid materials and occurs in a number of equations used for acoustical and vibration calculus the ratio of the imaginary part to the real part of complex poisson s ratio is referred to as poisson s loss factor the magnitude of the poisson s loss factor is investigated in this paper for homogeneous isotropic linear solid viscoelastic materials with positive poisson s ratio the relation of the poisson s loss factor to the material damping is determined it is shown that the magnitude of the poisson s loss factor is approximately proportional to the difference between the shear and bulk loss factors and is a rational fractional function of the dynamic poisson s ratio in addition relationships are developed which enable one to determine the approximate magnitude of the poisson s loss factor from knowledge only of the shear loss factor and the dynamic poisson s ratio it is shown that the poisson s loss factor is smaller than the shear loss factor usually by one order of magnitude at least moreover it is pointed out that the poisson s loss factor of a high loss and a low loss material may be about the same experimental data on two rubbers and a hard plastic are presented to verify the theoretical conclusions

existence of invariant manifolds for stochastic equations in infinite dimension we provide a frobenius type existence result for finite dimensional invariant submanifolds for stochastic equations in infinite dimension in the spirit of da prato and zabczyk 5 we recapture and make use of the convenient calculus on frechet spaces as developed by kriegl and michor 16 our main result is a weak version of the frobenius theorem on frechet spaces as an application we characterize all finite dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures a generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described here dynamic analysis is understood as transient analysis and frequency response analysis the generalized complex eigenvector method is based on nite element discretization of structure approximation of viscoelastic properties by di erential operators and mode superposition technique coe cients of di erential operator are de ned from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of di erential operator in preset frequency range advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range also the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions complex young s modulus complex poisson s ratio the method is veri ed with the help of comparing with solutions obtained by complex modulus method an in uence of viscoelastic poisson s ratio on transient and frequency responses of structure is demonstrated copyright 2001 john wiley sons ltd

invariance of closed convex cones for stochastic partial differential equations abstract the goal of this paper is to clarify when a closed convex cone is invariant for a stochastic partial differential equation spde driven by a wiener process and a poisson random measure and to provide conditions on the parameters of the spde which are necessary and sufficient

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

verification of local kramers kronig relations for complex modulus by means of fractional derivative model abstract the local kramers kronig k k relations which link the damping properties of solid materials at one frequency to the rate of frequency variation of dynamic modulus are not exact the validity and accuracy of the local k k relations is theoretically investigated in this paper by means of material models especially the fractional zener model it is shown that the local k k relations qualitatively always properly predict the relation between the damping and the frequency dependence of dynamic modulus for any type of deformation and any linear mechanism of energy loss determining the frequency variations nevertheless the accuracy depends on the rate of frequency variation of dynamic properties mainly of the loss modulus and loss factor and the weaker the frequency dependence the better the accuracy the accuracy is better than 10 if the slope of frequency increase or decrease of loss functions plotted in a log log system is smaller than 0 35 the application of the local k k relations to some experimental data is presented

existence of affine realizations for stochastic partial differential equations driven by levy processes the goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by levy processes admits an affine realization our results are accompanied by several examples arising in natural sciences and economics

an alternative approach on the existence of affine realizations for hjm term structure models we propose an alternative approach on the existence of affine realizations for heath jarrow and morton interest rate models it is applicable to a wide class of models and simultaneously it is conceptually rather comprehensible we also supplement some known existence results for particular volatility structures and provide further insights into the geometry of term structure models

identification of complex moduli and poisson s ratio from measured strains on an impacted bar identification of complex moduli and poisson s ratio from measured strains on an impacted bar

hamilton jacobi equations in infinite dimensions ii existence of viscosity solutions on demontre des resultats d existence generaux pour 2 problemes 1 le probleme de cauchy u t h x t u du 0 dans v 0 t u x 0 x dans v et 2 le probleme stationnaire u h x u du 0 dans v ou h et sont donnees

existence of affine realizations for levy term structure models we investigate the existence of affine realizations for term structure models driven by levy processes it turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps as special cases we study constant direction volatilities and the existence of short rate realizations

exit time problems in optimal control and vanishing viscosity method the authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first order hamilton jacobi hj equation up to the boundary this equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary when these solutions are equal they can be obtained through the vanishing viscosity method finally when the hj equation has a continuous solution it is proved to be the value function for the first exit time of the domain it is also the vanishing viscosity limit arising in particular in some large deviations problems

a variational method for identification of viscoelastic parameters from experimental data an identification method based on a variational algorithm is proposed for the determination of the viscoelastic properties of plates from a set of experimental data a pulse transmission configuration with parametric sources is used for the experimental measurements whereby two electrically mixed high frequency pulses are combined to generate a low frequency narrow beam signal to minimize the edge diffraction effect from a finite sized panel the variational method is based on an optimization technique adapted from an approach normally used in dynamics for the identification of motion parameters the fluid panel fluid system is initially represented by a transmission matrix model the model and the known experimental data are then used to build an optimization functional to be minimized by means of a collocation method based on the hamilton principle analogy the plate viscoelastic parameters are then calculated by application of well established numerical procedures to the resulting set of integral differential equations

path dependent hamilton jacobi equations in infinite dimensions abstract we propose notions of minimax and viscosity solutions for a class of fully nonlinear path dependent pdes with nonlinear monotone and coercive operators on hilbert space our main result is well posedness existence uniqueness and stability for minimax solutions a particular novelty is a suitable combination of minimax and viscosity solution techniques in the proof of the comparison principle one of the main difficulties the lack of compactness in infinite dimensional hilbert spaces is circumvented by working with suitable compact subsets of our path space as an application our theory makes it possible to employ the dynamic programming approach to study optimal control problems for a fairly general class of delay evolution equations in the variational framework furthermore differential games associated to such evolution equations can be investigated following the krasovski subbotin approach similarly as in finite dimensions

frequency dependences of complex moduli and complex poisson s ratio of real solid materials abstract the concept of a complex modulus of elasticity is a powerful and widely used tool for characterizing the linear dynamic elastic and damping properties of solid materials in the frequency domain it is shown in this paper that typical characters of frequency dependences of all complex moduli shear young s etc and complex poisson s ratios of real solid materials can be determined by transforming the causal and real relaxation and creep responses respectively from the time domain into the frequency domain even without having to specify the processes of relaxation and creep it is proved that all dynamic moduli monotonically increase and the dynamic poisson s ratio monotonically decreases with increasing frequency and all respective loss factors pass through at least one maximum these frequency dependences are generally valid for any real solid material regardless of the actual damping mechanisms some experimental results are presented and interpreted in the light of the theory the usefulness of theoretical predictions in materials engineering measurements of dynamic properties and in modelling dynamic behaviour is discussed