estimating dynamic equilibrium models using mixed frequency macro and financial data abstract we provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency along with macro series at standard lower frequency our formulation of the macro finance model in continuous time conveniently accounts for the difference in observation frequency we suggest the use of martingale estimating functions mef to infer the structural parameters of the model directly through a nonlinear scheme this method is compared to regression based methods and the generalized method of moments gmm we illustrate our approaches by estimating various versions of the ak vasicek model with mean reverting interest rates we provide asymptotic theory and monte carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of us macro and financial data

long memory continuous time models this paper presents a new family of long memory models the continuous time moving average fractional process the continuous time framework allows to reconcile two competitive types of modelling fractional integration of arma processes and fractional brownian motion a comparison with usual discrete time arfima models is lead some well known empirical evidence on macroeconomic and financial time series such as variability of forward rates aggregation of responses across heterogeneous agents are well captured by this continuous time modelling moreover the usual statistical tools for long memory series and for stochastic differential equations can be jointly applied in this setting

irreducible unitary representations of su 2 2 we give an explicit classification of the irreducible unitary representations of the simple lie group su 2 2

intertwining operators and unitary representations i abstract for a linear semisimple lie group with a compact cartan subgroup the authors obtain formulas for the action of intertwining operators on certain subspaces of standard induced representations these formulas provide explicit limitations on the pool of candidates for irreducible unitary representations since the only possible invariant inner product is given by such an intertwining operator

graphical models for marked point processes based on local independence summary a new class of graphical models capturing the dependence structure of events that occur in time is proposed the graphs represent so called local independences meaning that the intensities of certain types of events are independent of some but not necessarilly all events in the past this dynamic concept of independence is asymmetric similar to granger non causality so the corresponding local independence graphs differ considerably from classical graphical models hence a new notion of graph separation which is called separation is introduced and implications for the underlying model as well as for likelihood inference are explored benefits regarding facilitation of reasoning about and understanding of dynamic dependences as well as computational simplifications are discussed

godement jacquet l functions and full theta lifts we relate poles of local godement jacquet l functions to distributions on matrix spaces with singular supports as an application we show the irreducibility of the full theta lifts to mathrm gl n mathrm f of generic irreducible representations of mathrm gl n mathrm f where mathrm f is an arbitrary local field

a note on scaled variance ratio estimation of the hurst exponent with application to agricultural commodity prices abstract the measure of long term memory is important for the study of economic and financial time series this paper estimates the hurst exponent from a scaled variance ratio model for 17 commodity price series under the efficient market null h0 h 0 5 the distribution about the estimates of h are obtained from 90 95 and 99 confidence intervals generated from 20 000 monte carlo replications of a geometric brownian motion the results show that the scaled variance ratio provides a very good and stable estimate of the hurst exponent but the estimates can be quite different from the measure obtained from rescaled range or r s analysis in general commodity prices are consistent with the underlying assumption of a geometric brownian motion

the density of solutions to multifractional stochastic volterra integro differential equations abstract the aim of this paper is to study the density of solutions to stochastic volterra integro differential equations with multifractional noises we prove the existence of the density of solutions and show that the density is bounded by lower and upper gaussian bounds

intertwining operators into cohomology representations for semisimple lie groups abstract letgbe a semisimple lie group with finite center andlthe centralizer of a torus ing an explicit intertwining operator is constructed from a nonunitary principal series forginto dolbeault cohomology ong l the image lies in the space of strongly harmonic forms this paper generalizes results in l barchini a w knapp and r zierau j funct anal 107 1992 302 341 by replacing the one dimensional fiber overg lwith certain langlands quotients

discrete series characters and two structures let g be a connected semisimple real lie group with compact cartan subgroup harish chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators the main result of this paper is a new formula for these constants using two structures the new formula avoids endoscopy and stable discrete series entirely expressing unaveraged discrete series constants directly in terms of unaveraged discrete series constants corresponding to two structures of noncompact type

structural estimation of jump diffusion processes in macroeconomics this paper shows how to solve and estimate a continuous time dynamic stochastic general equilibrium dsge model with jumps it also shows that a continuous time formulation can make it simpler relative to its discrete time version to compute and estimate the deep parameters using the likelihood function when non linearities and or non normalities are considered we illustrate our approach by solving and estimating the stochastic ak and the neoclassical growth models our monte carlo experiments demonstrate that non normalities can be detected for this class of models moreover we provide strong empirical evidence for jumps in aggregate us data

a geometric realisation of tempered representations restricted to maximal compact subgroups let g be a connected linear real reductive lie group with compact centre let k g be maximal compact for a tempered representation pi of g we realise the restriction pi k as the k equivariant index of a dirac operator on a homogeneous space of the form g h for a cartan subgroup h g the result in fact applies to every standard representation such a space can be identified with a coadjoint orbit of g so that we obtain an explicit version of kirillov s orbit method for pi k in a companion paper we use this realisation of pi k to give a geometric expression for the multiplicities of the k types of pi in the spirit of the quantisation commutes with reduction principle this generalises work by paradan for the discrete series to arbitrary tempered representations

unitary representations induced from maximal parabolic subgroups abstract it is known that the problem of classifying the irreducible unitary representations of a linear connected semisimple lie group g comes down to deciding which langlands quotients j man v are infinitesimally unitary here man is any cuspidal parabolic subgroup is any discrete series or nondegenerate limit of discrete series representation of m and v is any complex valued linear functional on the lie algebra of a satisfying certain positivity and symmetry properties the authors determine which langlands quotients are infinitesimally unitary under the conditions that g is simple that dim a 1 and that g is neither split f 4 nor split g 2

optimal sobolev imbeddings involving rearrangement invariant quasinorms let m and n be positive integers with n 2 and 1 m n 1 we study rearrangement invariant quasinorms r and d on functions f 0 1 view the mathml source such that to each bounded domain in view the mathml sourcen with lebesgue measure there corresponds c c 0 for which one has the sobolev imbedding inequality r u t c d mu t u cm0 involving the nonincreasing rearrangements of u and a certain mth order gradient of u when m 1 we deal in fact with a closely related imbedding inequality of talenti in which d need not be rearrangement invariant r u t c d d dt x view the mathml sourcen u x u t u x dx u c10 in both cases we are especially interested in when the quasinorms are optimal in the sense that r cannot be replaced by an essentially larger quasinorm and d cannot be replaced by an essentially smaller one our results yield best possible refinements of such limiting sobolev inequalities as those of trudinger strichartz hansson brezis and wainger

small unitary representations of the double cover of sl m the irreducible unitary representations of the double cover sl m of the real group sl m with infinitesimal character p which are small in the sense that their annihilator in the universal enveloping algebra is maximal are expressed as langlands quotients of generalized principal series in the case where m is even we show that there are four such representations and in the case where m is odd there is just one the representations smallness allows them to be written as a sum of virtual representations leading to a character formula for their k types we investigate the place of these small representations in the orbit method and in the case of sl 2l 1 show that the representation is attached to a nilpotent coadjoint orbit the k type spectrum for the langlands quotients is explicitly determined and shown to be multiplicity free

intrinsic random functions and the paradox of l f noise by means of a generalized fejer theorem certain stationary increment random functions and random fields are shown to possess nonintegrable time invariant spectra the periodogram computed from a stationary increment process is shown to have the same sort of asymptotic statistical properties e g central limit theorem as the periodogram of a stationary process does these results throw light on the paradoxical nature of flicker noise and related phenomena that occur with random fields

boundary value maps szego maps and intertwining operators we consider one series of unitarizable representations the cohomological induced modules aq a with dominant regular infinitesimal character the minimal k type ir v of aq a determines a homogeneous vector bundle v g k the derived functor modules can be realized on the solution space of a first order differential operator da on v barchini knapp and zierau gave an explicit integral map s from the derived functor module realized in the langlands classification into the space of smooth sections of the vector bundle v g k in this paper we study the asymptotic behavior of elements in the image of s we obtain a factorization of the standard intertwining opeartors into the composition of the szego map s and a passage to boundary values 0 introduction let g be a linear connected semisimple lie group and let k be a maximal compact subgroup of g we assume that rank g rank k in this situation the cohomologically induced representation aq a with dominant regular infinitesimal character can be realized on solution spaces of invariant differential equations in g k see wo b 2 the minimal k type r v of aq a determines an homogeneous vector bundle vtr g k corresponding to certain choices of positive roots there is defined a certain homogeneous first order differential operator d on vtu in bkz and b 1 the authors gave an explicit nonzero integral map s from the derived functor module realized in the langlands classification to the space of smooth sections of the vector bundle vt g k the image of s is annihilated by the differential operator d when the representation under consideration is in the discrete series of g the differential operator vd coincides with schmid s differential operator s in this case the s transform was introduced by knapp and wallach in kw the realization of irreducible unitary representations in the g k picture generalizes bargmann s formulation of holomorphic discrete series of su 1 1 bar in terms of semisimple lie groups functions on the circle suggest non unitary principal series and holomorphic functions on the disk suggest discrete series representations the s transform in kw reduces in limiting cases limits of discrete series for su 1 1 to the szeg6 kernel for the disk see k 1 thus we call s a szeg6 map received by the editors february 17 1995 and in revised form october 9 1995 1991 mathematics subject classification primary 22c05 22e45 22e46 1997 american mathematical society 1877 this content downloaded from 207 46 13 124 on wed 22 jun 2016 05 42 59 utc all use subject to http about jstor org terms

fully measurable grand lebesgue spaces abstract using variable exponents we build a new class of rearrangement invariant banach function spaces independent of the variable lebesgue spaces whose function norm is f ess sup x 0 1 p x x f where p x denotes the norm of the lebesgue space of exponent p x assumed measurable and possibly infinite and is measurable too such class contains some known banach spaces of functions among which are the classical and the grand lebesgue spaces and the exp spaces 0 we analyze the function norm and we prove a boundedness result for the hardy littlewood maximal operator via a hardy type inequality

maximum likelihood estimation of linear continuous time long memory processes with discrete time data summary we develop a new class of time continuous autoregressive fractionally integrated moving average carfima models which are useful for modelling regularly spaced and irregularly spaced discrete time long memory data we derive the autocovariance function of a stationary carfima model and study maximum likelihood estimation of a regression model with carfima errors based on discrete time data and via the innovations algorithm it is shown that the maximum likelihood estimator is asymptotically normal and its finite sample properties are studied through simulation the efficacy of the approach proposed is demonstrated with a data set from an environmental study

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

discrete and continuous time cointegration we give a definition of integration and cointegration in continuous time and study characterizations of those definitions in particular for carma continuous time arma processes we check also that such singularities in carma processes may imply unit roots problems in the discretized corresponding process then error correction representations in continuous time are exhibited and discussed and a general theorem of representation giving a precise description of the singularities is proved lastly we look at other singularities emphasizing the importance of estimating the continuous time model if it is the true one a one dimensional noise can generate a two dimensional regular ar process

frequency domain estimation of temporally aggregated gaussian cointegrated systems this paper considers joint estimation of long run equilibrium coefficients and parameters governing the short run dynamics of a fully parametric gaussian cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic differential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the estimator of the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that of the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

error correction and long run equilibrium in continuous time this paper deals with error correction models ecm s and cointegrated systems that are formulated in continuous time long run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form so that there is no aliasing problem for these parameters the long run relationships are also preserved under quite general data filtering frequency domain procedures are outlined for estimation and inference these methods are asymptotically optimal under gaussian assumptions and they have the advantages of simplicity of computation and generality of specification thereby avoiding some methodological problems of dynamic specification in addition they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations models with restricted cointegrating matrices are also considered

knapp wallach szegő integrals ii the higher parabolic rank case let g be a connected reductive linear lie group with compact center and real rank 1 for each integer k 1 k 1 and each discrete series representation x of g an explicit embedding of g into a generalized principal series representation induced from a parabolic subgroup of rank k is given the existence of such embeddings was proved by w schmid in this paper an explicit integral formula with szegb kernel is given which provides these mappings

forecasting discrete stock and flow data generated by a second order continuous time system abstract this paper extends recent results on forecasting discrete stock and flow data generated by a continuous time model formulated as a system of second order stochastic differential equations an algorithm is presented for the computation of the forecasts and an expression for the asymptotic mean square error matrix of the forecasts is also derived these results when combined with the estimation algorithm in 1 provide a computationally efficient method of estimation forecasting and inference in continuous time systems

knapp wallach szego integrals and generalized principal series representations the parabolic rank one case abstract to each discrete series representation of a connected semisimple lie group g with finite center a g equivariant embedding into a generalized principal series representation is given this representation is induced from specified parameters on a maximal parabolic subgroup of g and the mapping is defined by an integral formula analogous to the szego integral introduced by knapp and wallach for a minimal parabolic subgroup in a limiting case embeddings of limits of discrete series representations are obtained and used to exhibit a reducibility theorem

cauchy szego maps invariant differential operators and some representations of su n 1 1 on considere des realisations concretes des groupes de lie et en particulier du groupe de lie semi simple su n 1 1

a spring block analogy for the dynamics of stock indexes abstract a spring block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes individual stocks are modeled by the blocks while the stock stock correlations are introduced via simple elastic forces acting in the springs the dragging effect of the moving belt corresponds to the expected economic growth the spring block system produces collective behavior and avalanche like phenomena similar to the ones observed in stock markets an artificial index is defined for the spring block chain and its dynamics is compared with the one measured for the dow jones industrial average for certain parameter regions the model reproduces qualitatively well the dynamics of the logarithmic index the logarithmic returns the distribution of the logarithmic returns the avalanche size distribution and the distribution of the investment horizons a noticeable success of the model is that it is able to account for the gain loss asymmetry observed in the inverse statistics our approach has mainly a pedagogical value bridging between a complex socio economic phenomena and a basic mechanical model in physics

long memory via networking many time series exhibit long memory their autocorrelation function decays slowly with lag this behavior has traditionally been modeled via unit roots or fractional brownian motion and explained via aggregation of heterogeneous processes nonlinearity learning dynamics regime switching or structural breaks this paper identifies a different and complementary mechanism for long memory generation by showing that it can naturally arise when a large number of simple linear homogeneous economic subsystems with short memory are interconnected to form a network such that the outputs of the subsystems are fed into the inputs of others this networking picture yields a type of aggregation that is not merely additive resulting in a collective behavior that is richer than that of individual subsystems interestingly the long memory behavior is found to be almost entirely determined by the geometry of the network while being relatively insensitive to the specific behavior of individual agents

the langlands parameters of subquotients of certain derived functor modules letgbe a noncompact simple lie group with finite center letkbe a maximal compact subgroup and let g0 k0 p0be the corresponding decomposition of the lie algebra suppose rank g rank k and let t0be a compact cartan subalgebra and b be a borel subalgebra letab be a derived functor module with infinitesimal character which is nondominant with respect to a noncompact simple root suppose that 2 p iskdominant so that thektype with highest weight occurs with multiplicity one inab we develop conditions on the roots of g under which a functor of cohomological induction maps a certain module of parabolic induction to another module of parabolic induction extending a result due to vogan this allows us in many cases to determine the langlands parameters of the subquotient ofab containing via a conjectured method of knapp

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

compositions of theta correspondences theta correspondence y over r is established by howe j amer math soc 2 1989 535 in he j funct anal 199 2003 92 we prove that y preserves unitarity under certain restrictions generalizing the result of li invent math 97 1989 237 the goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences we show that under a natural condition on the sizes of the related dual pairs which can be predicted by the orbit method j algebra 190 1997 518 representation theory of lie groups park city 1998 pp 179 238 the orbit correspondence for real and complex reductive dual pairs preprint 2001 one can compose theta correspondences to obtain unitary representations we call this process quantum induction r 2004 published by elsevier inc msc primary 22e45 22e46

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

stochastic calculus with respect to gaussian processes in this paper we develop a stochastic calculus with respect to a gaussian process of the form b t int t 0 k t s dw s where w is a wiener process and k t s is a square integrable kernel using the techniques of the stochastic calculus of variations we deduce change of variable formulas for the indefinite integrals and we study the approximation by riemann sums the particular case of the fractional brownian motion is discussed

an improvement of dimension free sobolev imbeddings in r i spaces abstract we prove a dimension invariant imbedding estimate for sobolev spaces of first order into a small lebesgue space and we establish the optimality of its fundamental function namely for any 1 p the inequality f y p 0 1 c p f l p b n f w 0 1 p b n n p where y p 0 1 is a rearrangement invariant banach function space independent of the dimension n b n is the ball in r n of measure 1 and c p is a constant independent of n is satisfied by the small lebesgue space l p p 2 0 1 moreover we show that the smallest space y p 0 1 in the sense of the continuous imbedding such that is true has the fundamental function equivalent to that of l p p 2 0 1 as a byproduct of our results we get that the space l p log l p 2 is optimal in the framework of the orlicz spaces satisfying

frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data this paper proposes a simple method for exploiting the information contained in mixed frequency and mixed sample data in the estimation of cointegrating vectors the asymptotic properties of easy to compute spectral regression estimators of the cointegrating vectors are derived and these estimators are shown to belong to the class of optimal cointegration estimators furthermore wald statistics based on these estimators have asymptotic chi square distributions which enable inferences to be made straightforwardly simulation experiments suggest that the spectral regression estimators considered perform well in finite samples and are at least as good as time domain fully modified estimators the finite sample size and power properties of the spectral regression based wald statistic are also found to be good

the exceptional lie algebra e7 25 multiplets and invariant differential operators in the present paper we continue the project of systematic construction of invariant differential operators on the example of the non compact exceptional algebra e7 25 our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras which we call conformal lie algebras which have very similar properties to the conformal algebras of n dimensional minkowski spacetime this class of algebras is identified and summarized in a table another motivation is related to the ads cft correspondence we give the multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators

long memory volatility in derivative hedging abstract the aim of this work is to take into account the effects of long memory in volatility on derivative hedging this idea is an extension of the work by fedotov and tan stochastic long memory process in option pricing int j theor appl finance 8 2005 381 392 where they incorporate long memory stochastic volatility in option pricing and derive pricing bands for option values the starting point is the stochastic black scholes hedging strategy which involves volatility with a long range dependence the stochastic hedging strategy is the sum of its deterministic term that is classical black scholes hedging strategy with a constant volatility and a random deviation term which describes the risk arising from the random volatility using the fact that stock price and volatility fluctuate on different time scales we derive an asymptotic equation for this deviation in terms of the green s function and the fractional brownian motion the solution to this equation allows us to find hedging confidence intervals

isoperimetry and symmetrization for logarithmic sobolev inequalities abstract using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic sobolev inequalities in particular we obtain new gaussian symmetrization inequalities and connect them with logarithmic sobolev inequalities our methods are very general and can be easily adapted to more general contexts

principal component analysis of high frequency data we develop the necessary methodology to conduct principal component analysis at high frequency we construct estimators of realized eigenvalues eigenvectors and principal components and provide

new properties of small lebesgue spaces and their applications we prove some new properties of the small lebesgue spaces introduced by fiorenza in f combining these properties with the poincare sobolev inequalities for the relative rearrangement see r1 we derive some new and precises estimates either for small lebesgue sobolev spaces or for quasilinear equations with data in the small lebesgue spaces

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

pointwise symmetrization inequalities for sobolev functions and applications we develop a technique to obtain new symmetrization inequalities that provide a unified framework to study sobolev inequalities concentration inequalities and sharp integrability of solutions of elliptic equations

gradient type differential operators and unitary highest weight representations of su p q abstract let c p q be equipped with a hermitian form of signature p q and let su p q denote the subgroup of the corresponding invariance group u p q consisting of matrices with determinant 1 to certain highest weights we associate a first order group invariant linear differential operator d whose kernel contains a unitary highest weight representation with highest weight the fock model realization of unitary highest weight representations of u p q is the fundamental tool used to implement this construction the operator d is shown to be equivalent to an operator d which acts on hol g k h the space of holomorphic vector valued functions defined on g k we identify a set 1 of highest weights such that ker d is a proper subspace of hol g k h and show that those in 1 correspond to points occurring at the far right of the discrete set in the classification scheme of enright howe and wallach first order differential equations arising from this proper containment are explicitly derived from the operator d we illustrate the fundamental nature of these first order equations by deriving from them a system which completely determines the irreducible spaces for ladder representations of su p q

strata hasse invariants hecke algebras and galois representations we construct group theoretical generalizations of the hasse invariant on strata closures of the stacks mathop g hbox mathtt zip nolimits mu restricting to zip data of hodge type we obtain a group theoretical hasse invariant on every ekedahl oort stratum closure of a general hodge type shimura variety a key tool is the construction of a stack of zip flags mathop g hbox mathtt zipflag nolimits mu fibered in flag varieties over mathop g hbox mathtt zip nolimits mu it provides a simultaneous generalization of the classical case homogeneous complex manifolds studied by griffiths schmid and the flag space for siegel varieties studied by ekedahl van der geer four applications are obtained 1 pseudo representations are attached to the coherent cohomology of hodge type shimura varieties modulo a prime power 2 galois representations are associated to many automorphic representations with non degenerate limit of discrete series archimedean component 3 it is shown that all ekedahl oort strata in the minimal compactification of a hodge type shimura variety are affine thereby proving a conjecture of oort 4 part of serre s letter to tate on mod p modular forms is generalized to general hodge type shimura varieties

stochastic fractional evolution equations with fractional brownian motion and infinite delay abstract in this paper we consider a class of stochastic fractional evolution equations with infinite delay and a fractional brownian motion in a hilbert space by the stochastic analysis technique we establish the existence and uniqueness of mild solutions for these equations under non lipschitz condition with lipschitz conditions being considered as a special case an example is provided to illustrate the theory

on the howe correspondence for symplectic orthogonal dual pairs we reformulate some of moeglin s results on the correspondence for the dual pairs sp 2n r o p q with p and q even and fill in the cases where p and q are both odd we arrive at a complete and detailed description in terms of langlands parameters of the dual pair correspondence for the cases p q 2n and p q 2n 2 in addition we point out and suggest a way to correct an error in moeglin s paper

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

frequency domain gaussian estimation of temporally aggregated cointegrated systems this paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain gaussian estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

on dimension free sobolev imbeddings i abstract we prove dimension invariant imbedding theorems for sobolev spaces using the gross logarithmic inequality

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

a twisted invariant paley wiener theorem for real reductive groups let g be the group of real points of a possibly disconnected linear reductive algebraic group defined over r which is generated by the real points of a connected component g let k be a maximal compact subgroup of the group of real points of the identity component of this algebraic group we characterize the space of maps 7 tr f where is an irreducible tempered representation of g and f varies over the space of smooth compactly supported functions on g which are leftand right k finite this work is motivated by applications to the twisted arthur selberg trace formula

a direct approach to the duality of grand and small lebesgue spaces abstract in this paper we show by elementary methods that the quasinorms of the grand and small lebesgue spaces f l p sup 0 t 1 1 log t 1 p t 1 f s p d s 1 p 1 p f l q 0 1 1 log t 1 q 0 t f s q d s 1 q d t t q p p 1 found by fiorenza and karadzhov in a fiorenza g e karadzhov grand and small lebesgue spaces and their analogs z anal anwendungen 23 4 2004 657 681 by using deeply extrapolation interpolation techniques are associate each other in other terms the sharp holder s type inequality 0 1 f g d x c p f l q g l p is proven where the sharpness means that l q is the smallest quasinorm up to equivalences such that the inequality holds the method is based entirely on integral estimates makes use of asymptotic properties of euler s gamma function and gives an explicit estimate of the constant c p all the results are expressed in terms of the more general spaces l p and l q 0

mixed scale jump regressions with bootstrap inference abstract we develop an efficient mixed scale estimator for jump regressions using high frequency asset returns a fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio a coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets the proposed estimator has a non standard asymptotic distribution that cannot be made asymptotically pivotal via studentization we propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity we show that the bootstrap provides an automatic higher order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation the monte carlo analysis indicates good finite sample performance of the general specification test and confidence intervals based on the bootstrap we apply the method to a high frequency panel of dow stock prices together with the market index defined by the s p 500 index futures over the period 2007 2014 we document remarkable temporal stability in the way that stocks react to market jumps however this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector specific jump events

schubert cells and representation theory let g be a linear real reductive group and let p be a parabolic subgroup the bruhat decomposition of g gives a cellular decomposition of the generalized flag manifold x g p originating in the work of schubert on grassmann manifolds this cellular decomposition was used by ehresmann eh to give a proof of the basis theorem for the integral cohomology of grassmannians since ehresmann it has been clear that for a generalized flag manifold x a more detailed understanding of this decomposition by generalized schubert cells would provide a determination of the integral co homology of x the aim of this article is to give a representation theoretic determination of the differentials in the schubert cell decomposition of x and thereby obtain a combinatorial description of the integral co homology of x our primary tool will be the infinite dimensional representation theory of g if g and p are complex groups elementary considerations show that all schubert cells define non zero integral homology classes and that none are torsion moreover the cohomology has the well known connection to finitedimensional representation theory ct ko1 ko2 bt for real groups g and p even in low dimensions torsion can be present in the homology of real flag manifolds thus the major new development in this paper is that the infinite dimensional representation theory of g detects which real schubert cells define integral in particular torsion classes in the co homology the innovation on the representation theoretic side that makes possible the consideration of co homology with integer coefficients is the geometric formulation of representation theory introduced by beilinson bernstein to compute homology we use a topological technique that applies to spaces with filtration let x p be the union of schubert cells whose dimension

weight filtrations for induced representations of real reductive lie groups soit g un groupe matriciel reel semi simple connexe et p man la decomposition de langlands d un sous groupe parabolique de g etant donnee une representation admissible de m et un caractere e de a on peut former la representation induite normalisee ip e de g on decrit une g filtration de ip e avec des sous quotients semi simples en termes d une m filtration connue a priori de a sous quotients semi simples dans le cas de caractere infinitesimal entier

nonlinearity and temporal dependence nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models we study this link using three measures of temporal dependence mixing mixing and mixing stationary diffusions that are mixing have mixing coefficients that decay exponentially to zero when they fail to be mixing they are still mixing and mixing but coefficient decay is slower than exponential for such processes we find transformations of the markov states that have finite variances but infinite spectral densities at frequency zero the resulting spectral densities behave like those of stochastic processes with long memory finally we show how state dependent poisson sampling alters the temporal dependence

on the analogy between real reductive groups and cartan motion groups contraction of irreducible tempered representations attached to any reductive lie group g is a cartan motion group g 0 a lie group with the same dimension as g but a simpler group structure a natural one to one correspondence between the irreducible tempered representations of g and the unitary irreducible representations of g 0 whose existence had been suggested by mackey in the 1970s has recently been described by the author in the present notes we use the existence of a family of groups interpolating between g and g 0 to realize the bijection as a deformation for every irreducible tempered representation pi of g we build in an appropriate fr echet space a family of subspaces and evolution operators that contract pi onto the corresponding representation of g 0

fully measurable small lebesgue spaces abstract we build a new class of banach function spaces whose function norm is p f inf f k 1 f k k 1 ess inf x 0 1 p x x 1 f k where p x denotes the norm of the lebesgue space of exponent p x assumed measurable and possibly infinite constant with respect to the variable of f and is measurable too such class contains some known banach spaces of functions among which are the classical and the small lebesgue spaces and the orlicz space l log l 0 furthermore we prove the following holder type inequality 0 1 f g d t p f p g where p f is the norm of fully measurable grand lebesgue spaces introduced by anatriello and fiorenza in 2 for suitable choices of p x and x it reduces to the classical holder s inequality for the spaces e x p 1 and l log l 0

limits of discrete series with infinitesimal character zero for a connected linear semisimple lie group this paper considers those nonzero limits of discrete series representations having infinitesimal character 0 calling them totally degenerate such representations exist if and only if has a compact cartan subgroup is quasisplit and is acceptable in the sense of harish chandra totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms in fact those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of galois groups of number fields the automorphic representations in question have important arithmetic significance but very little has been proved up to now toward establishing this part of the langlands conjectures there is some hope of making progress in this area and for that one needs to know in detail the representations of under consideration the aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the knapp zuckerman classification of irreducible tempered representations i e to express these representations as induced representations with nondegenerate data the paper uses a general argument based on the finite abelian reducibility group attached to a specific unitary principal series representation of first an easy result gives the aggregate of the classification parameters then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation by representation fashion the paper includes tables of the classification parameters for all such groups

the estimation of continuous time models with mixed frequency data this paper derives exact representations for discrete time mixed frequency data generated by an underlying multivariate continuous time model allowance is made for different combinations of stock and flow variables as well as deterministic trends and the variables themselves may be stationary or nonstationary and possibly cointegrated the resulting discrete time representations allow for the information contained in high frequency data to be utilised alongside the low frequency data in the estimation of the parameters of the continuous time model monte carlo simulations explore the finite sample performance of the maximum likelihood estimator of the continuous time system parameters based on mixed frequency data and a comparison with extant methods of using data only at the lowest frequency is provided an empirical application demonstrates the methods developed in the paper and it concludes with a discussion of further ways in which the present analysis can be extended and refined

a nonnested approach to testing continuous time models against discrete alternatives abstract this paper considers a test of two competing models when one is formulated in continuous time as a system of stochastic differential equations and the other is formulated in discrete time as a system of nonlinear equations since the competing hypotheses are nonnested the appropriate formulae are derived for the implementation of the cox test this approach is illustrated with an application to the demand for food and related products in the united kingdom