adaptive estimation of the dynamics of a discrete time stochastic volatility model abstract this paper is concerned with the discrete time stochastic volatility model y i exp x i 2 i x i 1 b x i x i i 1 where only y i is observed the model is rewritten as a particular hidden model z i x i e i x i 1 b x i x i i 1 where i and e i are independent sequences of i i d noise moreover the sequences x i and e i are independent and the distribution of e is known then our aim is to estimate the functions b and 2 when only observations z 1 z n are available we propose to estimate b f and b 2 2 f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces by ratio strategy estimators of b and 2 are then deduced the mean square risk of the resulting estimators are studied and their rates are discussed lastly simulation experiments are provided constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples

optimal model selection for stationary data under various mixing conditions we build penalized least squares estimators of the marginal density of a stationary process using the slope algorithm and resampling penalties when the data are beta or tau mixing these estimators satisfy oracle inequalities with leading constant asymptotically equal to 1

existence and homogenization of nonlinear elliptic systems in nonreflexive spaces abstract we consider a strongly nonlinear elliptic problem with the homogeneous dirichlet boundary condition the growth and the coercivity of the elliptic operator is assumed to be indicated by an inhomogeneous anisotropic n function first an existence result is shown under the assumption that the n function or its convex conjugate satisfies 2 condition the second result concerns the homogenization process for families of strongly nonlinear elliptic problems with the homogeneous dirichlet boundary condition under above stated conditions on the elliptic operator which is additionally assumed to be periodic in the spatial variable

a pocket guide to nonlinear differential equations in musielak orlicz spaces abstract the musielak orlicz setting unifies variable exponent orlicz weighted sobolev and double phase spaces they inherit technical difficulties resulting from general growth and inhomogeneity in this survey we present an overview of developments of the theory of existence of pdes in the setting including reflexive and non reflexive cases as well as isotropic and anisotropic ones particular attention is paid to problems with data below natural duality in absence of lavrentiev s phenomenon

limiting spectral distribution of gram matrices associated with functionals of β mixing processes we give asymptotic spectral results for gram matrices of the form n 1 x n x t n where the entries of x n are dependent across both rows and columns and that are functionals of absolutely regular sequences and have only finite second moments we derive under mild dependence conditions in addition to an arithmetical decay condition on the mixing coefficients an integral equation of the stieltjes transform of the limiting spectral distribution of n 1 x n x t n in terms of the spectral density of the underlying process applications to examples of positive recurrent markov chains and dynamical systems are also given

steady flow of non newtonian fluids monotonicity methods in generalized orlicz spaces abstract our purpose is to show the existence of weak solutions to steady flow of non newtonian incompressible fluids with nonstandard growth conditions of the cauchy stress tensor we are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening since l p framework is not sufficient to capture the described model we describe the growth conditions with the help of a general x dependent convex function and formulate our problem in generalized orlicz spaces

hyperbolic groups and their quotients of bounded exponents in 1987 gromov conjectured that for every non elementary hyperbolic group g there is an n n g such that the quotient group g gn is infinite the article confirms this conjecture in addition a description of finite subgroups of g gn is given it is proven that the word and conjugacy problem are solvable in g gn and that k 1g k 1 the proofs heavily depend upon prior authors results on the gromov conjecture for torsion free hyperbolic groups and on the burnside problem for periodic groups of even exponents

fine properties of functions with bounded deformation the paper is concerned with the fine properties of functions in the space of functions with bounded deformation we analyse the set of lebesgue points and the set where these functions have one sided approximate limits moreover following the analogy with we decompose the symmetric distributional derivative into an absolutely continuous part a jump part and a cantor part the main result of the paper is a structure theorem for functions showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections moreover we prove that functions are approximately differentiable in almost every point of their domain

rosenthal type inequalities for the maximum of partial sums of stationary processes and examples the aim of this paper is to propose new rosenthal type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations as in the recent results by peligrad et al proc amer math soc 135 2007 541 550 and rio j theoret probab 22 2009 146 163 the estimates of the moments are expressed in terms of the norms of projections of partial sums the proofs of the results are essentially based on a new maximal inequality generalizing the doob maximal inequality for martingales and dyadic induction various applications are also provided

on flows of an incompressible fluid with a discontinuous power law like rheology we establish the mathematical theory for steady and unsteady flows of fluids with discontinuous constitutive equations we consider a model for a fluid that at certain critical values of the shear rate exhibits jumps in the generalized viscosity of a power law type using tools such as young measures maximal monotone operators compact embeddings and energy equality we prove the existence of a solution to the problem under consideration in this approach galerkin approximations converge strongly to the solution of the original problem

nonlinear parabolic problems in musielak orlicz spaces abstract our studies are directed to the existence of weak solutions to a parabolic problem containing a multi valued term the problem is formulated in the language of maximal monotone graphs we assume that the growth and coercivity conditions of a nonlinear term are prescribed by means of a time and space dependent n function this results in the formulation of the problem in generalized musielak orlicz spaces we are using density arguments hence an important step of the proof is a uniform boundedness of appropriate convolution operators in musielak orlicz spaces for this purpose we shall need to assume a kind of logarithmic holder regularity with respect to t and x

generalized orlicz spaces and related pde abstract we prove the boundedness of the maximal operator in generalized orlicz spaces defined on subsets of r n the proof is based on an extension result for functions we study generalized sobolev orlicz spaces and establish density of smooth functions and the poincare inequality as applications we establish the existence of solutions of the laplace equation with zero and non zero right hand side further we systematize assumptions for functions and prove several basic tools needed for the study of differential equations of generalized orlicz growth

copula based time series with filtered nonstationarity abstract economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously this paper studies copula based time series models that capture both patterns we introduce a procedure where nonstationarity is removed via a filtration and then the nonlinear temporal dependence in the filtered data is captured via a flexible markov copula we propose two estimators of the copula dependence parameters the parametric two step copula estimator where the marginal distribution of the filtered series is estimated parametrically and the semiparametric two step copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series we show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation and may be non normal surprisingly the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration which is normal and free of marginal distribution specification the simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas and facilitate statistical inferences such as hypothesis testing and model selection tests on semiparametric copula based dynamic models in the presence of nonstationarity monte carlo studies and real data applications are presented

peripheral fillings of relatively hyperbolic groups in this paper a group theoretic version of dehn surgery is studied starting with an arbitrary relatively hyperbolic group g we define a peripheral filling procedure which produces quotients of g by imitating the effect of the dehn filling of a complete finite volume hyperbolic 3 manifold m on the fundamental group 1 m the main result of the paper is an algebraic counterpart of thurston s hyperbolic dehn surgery theorem we also show that peripheral subgroups of g almost have the congruence extension property and the group g is approximated in an algebraic sense by its quotients obtained by peripheral fillings

the equivalence of some residual properties of word hyperbolic groups abstract we show that every word hyperbolic group is residually finite if and only if every word hyperbolic group has a finite quotient

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

existence of renormalized solutions to elliptic equation in musielak orlicz space abstract we prove existence of renormalized solutions to general nonlinear elliptic equation in musielak orlicz space avoiding growth restrictions namely we consider div a x u f l 1 on a lipschitz bounded domain in r n the growth of the monotone vector field a is controlled by a generalized nonhomogeneous and anisotropic n function m the approach does not require any particular type of growth condition of m or its conjugate m neither 2 nor 2 the condition we impose is log holder continuity of m which results in good approximation properties of the space the proof of the main results uses truncation ideas the young measures methods and monotonicity arguments

strongly nonlinear parabolic equations with natural growth terms in orlicz spaces abstract we prove approximation and compactness results in inhomogeneous orlicz sobolev spaces and look at as an application the cauchy dirichlet equation u a u g x t u u f w 1 x e m where a is a leray lions operator having a growth not necessarily of polynomial type we also give a trace result allowing to deduce the continuity of the solutions with respect to time

cartesian currents weak diffeomorphisms and existence theorems in nonlinear elasticity in this paper we introduce some new classes of functions among these a class of weak diffeomorphisms in these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals in particular we prove the existence of one to one orientation preserving maps that minimize suitable energies associated with hyperelastic materials the minimizers are also proved to satisfy equilibrium equations finally radial deformations are discussed in connection with cavitation

new martingale inequalities and applications to fourier analysis abstract let f p be a probability space and 0 0 be a musielak orlicz function in this article the authors prove that the doob maximal operator is bounded on the musielak orlicz space l using this and extrapolation method the authors then establish a fefferman stein vector valued doob maximal inequality on l as applications the authors obtain the dual version of the doob maximal inequality and the stein inequality for l which are new even in weighted orlicz spaces the authors then establish the atomic characterizations of martingale musielak orlicz hardy spaces h s p q h s and h m from these atomic characterizations the authors further deduce some martingale inequalities between different martingale musielak orlicz hardy spaces which essentially improve the corresponding results in orlicz space case and are also new even in weighted orlicz spaces by establishing the davis decomposition on h s and h m the authors obtain the burkholder davis gundy inequality associated with musielak orlicz functions finally using the previous martingale inequalities the authors prove that the maximal fejer operator is bounded from h 0 1 to l 0 1 which further implies some convergence results of the fejer means these results are new even for the weighted hardy spaces

inequalities for absolutely regular sequences application to density estimation this paper investigates the problem of density estimation for absolutely regular observations in a first part we state two important results a new variance inequality and a rosenthal type inequality this allows us to study the p integrated risk p 2 of a large class of density estimators including kernel or projection estimators under the summability condition on the mixing coefficients k 0 k 1 p 2 k the rates obtained are those known to be optimal in the independent setting

an imbedding theorem for musielak sobolev spaces abstract let be a bounded domain in r n and a c 1 0 0 be a musielak orlicz function we established an imbedding theorem for the musielak sobolev space w 1 a of the form w 1 a l a where a is the sobolev conjugate function of a a musielak orlicz function defined in the paper this theorem extends the imbedding theorem established by donaldson and trudinger for orlicz sobolev spaces to the case of musielak sobolev spaces

on finite and locally finite subgroups of free burnside groups of large even exponents the following basic results on infinite locally finite subgroups of a freem generator burnside groupb m n of even exponentn wherem 1 andn 248 nis divisible by 29 are obtained a clear complete description of all infinite groups that are embeddable inb m n as maximal locally finite subgroups is given any infinite locally finite subgroup l ofb m n is contained in a unique maximal locally finite subgroup while any finite 2 subgroup ofb m n is contained in continuously many pairwise nonisomorphic maximal locally finite subgroups in addition l is locally conjugate to a maximal locally finite subgroup ofb m n to prove these and other results centralizers of subgroups inb m n are investigated for example it is proven that the centralizer of a finite 2 subgroup ofb m n contains a subgroup isomorphic to a free burnside groupb n of countably infinite rank and exponentn the centralizer of a finite non 2 subgroup ofb m n or the centralizer of a nonlocally finite subgroup ofb m n is always finite the centralizer of a subgroup s is infinite if and only if s is a locally finite 2 group

on the relaxation in bv ω rm of quasi convex integrals abstract given a quasi convex function f with linear growth we find the integral representation in bv r m of the functional f arising from the relaxation of f u f u dx u c 1 r m in the l loc 1 r m topology

renormalized solutions to nonlinear parabolic problems in generalized musielak orlicz spaces abstract we will present the proof of existence of renormalized solutions to a nonlinear parabolic problem t u div a d u f with right hand side f and initial data u 0 in l 1 the growth and coercivity conditions on the monotone vector field a are prescribed by a generalized n function m which is anisotropic and inhomogeneous with respect to the space variable in particular m does not have to satisfy an upper growth bound described by a 2 condition therefore we work with generalized musielak orlicz spaces which are not necessarily reflexive moreover we provide a weak sequential stability result for a more general problem t u div a d u f u f where is a monotone function with respect to the second variable and f is locally lipschitz continuous within the proof we use truncation methods young measure techniques the integration by parts formula and monotonicity arguments which have been adapted to nonreflexive musielak orlicz spaces

adaptive estimation in autoregression or mixing regression via model selection we study the problem of estimatingsome unknown regression function in a beta mixing dependent framework to this end we consider some collection of models which are finite dimensional spaces a penalized least squares estimator plse is built on a data driven selected model among this collection we state non asymptotic risk bounds for this plse and give several examples where the procedure can be applied autoregression regression with arithmetically beta mixing design points regression with mixing errors estimation in additive frameworks estimation of the order of the autoregression in addition we show that under a weak moment condition on the errors our estimator is adaptive in the minimax sense simultaneously over some family of besov balls

processus empiriques absolument reguliers et entropie universelle nous etendons le theoreme limite central fonctionnel de pollard pour les processus empiriques indexes par des familles de fonctions d entropie universelle integrable aux suites d observations absolument regulieres et stationnaires sous des conditions d entropie universelles sur raisonnables nous montrons un theoreme limite central uniforme pour les suites de variables aleatoires absolument regulieres et stationnaires sous la condition minimale de sommabilite des coefficients de melange n n

new dependence coefficients examples and applications to statistics to measure the dependence between a real valued random variable x and a algebra we consider four distances between the conditional distribution function of x given and the distribution function of x the coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations in particular we show that they are well adapted to functions of mixing sequences iterated random functions and dynamical systems starting from a new covariance inequality we study the mean integrated square error for estimating the unknown marginal density of a stationary sequence we obtain optimal rates for kernel estimators as well as projection estimators on a well localized basis under a minimal condition on the coefficients using recent results we show that our coefficients may be also used to obtain various exponential inequalities a concentration inequality for lipschitz functions and a berry esseen type inequality

on the bass lubotzky question about quotients of hyperbolic groups abstract we prove at theorem 1 that any non elementary hyperbolic group g possesses a non trivial finitely presented quotient q having no non trivial subgroups of finite indices the theorem was commissioned in august 1997 by h bass and a lubotzky because the statement was required to constructing of their counter examples to platonov s conjecture on the representation rigid linear groups bl theorem 2 gives three equivalent reformulations of the known problem on existence of non residually finite hyperbolic groups

a geometrical approach to monotone functions in r n this paper is concerned with the fine properties of monotone func tions on r n we study the continuity and differentiability properties of these functions the approximability properties the structure of the distributional derivatives and of the weak jacobians moreover we exhibit an example of a monotone function u which is the gradient of a c 1 convex function and

renormalized solutions to parabolic equations in time and space dependent anisotropic musielak orlicz spaces in absence of lavrentiev s phenomenon abstract the paper concerns existence and uniqueness of solutions to a nonlinear parabolic equation with merely integrable data on a lipschitz bounded domain in r n our focal point is to involve the leading nonlinear part of the operator whose growth is described by anisotropic n function m inhomogeneous in the space and the time variables the main goals are proven in absence of lavrentiev s phenomenon to ensure which we impose a certain type of balance of interplay between the behavior of m for large and small changes of time and space variables its instances are log holder continuity of variable exponent inhomogeneous in time and space or optimal closeness condition for powers in double phase spaces possibly changing in time new delicate approximation in time result is proven and applied in the construction of renormalized solutions

acylindrically hyperbolic groups with exotic properties abstract we prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient as an application we obtain an acylindrically hyperbolic group q with strong fixed point properties q has property f l p for all p 1 and every action of q on a finite dimensional contractible topological space has a fixed point in addition q has other properties which are rather unusual for groups exhibiting hyperbolic like behavior e g q is not uniformly non amenable and has finite generating sets with arbitrary large balls consisting of torsion elements

a bernstein type inequality and moderate deviations for weakly dependent sequences in this paper we present a bernstein type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded the class considered includes geometrically and subgeometrically strongly mixing sequences the result is then used to derive asymptotic moderate deviation results applications are given for classes of markov chains iterated lipschitz models and functions of linear processes with absolutely regular innovations