tightness of products of random matrices and stability of linear stochastic systems soit n la distribution d un produit de n matrices aleatoire i i d on etudie la compacite et la convergence de la suite n n on l applique aux equations differentielles stochastiques lineaires

a dimension formula for bernoulli convolutions we present a dynamical approach to the study of the singularity of infinitely convolved bernoulli measuresv for the golden section we introducev as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square the fat baker s transformation our approach strongly relies on the markov structure of the underlying dynamical system indeed if golden mean the fat baker s transformation has a very simple markov coding the ambiguity of order two of this coding which appears when projecting on the line due to passages for the central overlapping zone can be expressed by means of products of matrices of order two this product has a markov distribution inherited by the markov structure of the map the dimension of the projected measure is therefore associated to the growth of this product our dimension formula appears in a natural way as a version of the furstenberg guivarch formula our technique provides an explicit dimension formula and most important provides a formalism well suited for the multifractal analysis of this measure as we will show in a forthcoming paper

tightness of products of i i d random matrices ii in this paper we prove a necessary and sufficient condition for tightness of products of i i d finite dimensional random real matrices we give an example illustrating the use of our theorem and treat in more details the case of 2 x 2 real matrices

a nonlinear autoregressive conditional duration model with applications to financial transaction data abstract this paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration acd model considered in engle and russell econometrica 66 5 1998 1127 1162 we propose a threshold autoregressive conditional duration tacd model to allow the expected duration to depend nonlinearly on past information variables conditions for the tacd process to be ergodic and existence of moments are established strong evidence is provided to suggest that fast transacting periods and slow transacting periods of nyse stocks have quite different dynamics based on the improved model we identify multiple structural breaks in the transaction duration data considered and those break points match nicely with real economic events

convergence in distribution of products of d d random matrices abstract in this paper we present limit theorems on the convergence in distribution of products of i i d matrices based on easily verifiable conditions on the support of the distribution

recurrent random walks in nonnegative matrices ii in this paper we continue the study undertaken in our earlier paper m1 one of the main results here can be described as follows letx0 x1 be a sequence of iid random affine maps from r d into itself let us write w n x n x n 1 x0 andz n x0x1 x n where composition of maps is the rule of multiplication by the attractora u u r d we mean the setau y r d p wnu n i o 0 for every openn containingy it is shown that the attractora u under mild conditions is the support of a stationary probability measure when the random walk z n has at least one recurrent state

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given

convergence in distribution of products of random matrices a semigroup approach on considere le probleme de la convergence faible de la suite des puissances de convolution d une mesure de probabilite dans le contexte general d un semigroupe non compact

on a pathology in indefinite metric inner product space a pathology related to an indefinite metric which has been pointed out by ito in connection with construction of a two dimensional quantum field model at a finite cutoff is mathematically analyzed in a simple model it is found for a model hamiltonian with a parameter in an indefinite metric inner product space that eigenvalues with a complete set of eigenvectors changes suddenly from positive integers to negative integers as a parameter crosses a critical value the hamiltonian being skew selfadjoint with absolutely continuous spectrum on a pure imaginary axis at the critical value of the parameter if a fixed positive definite hilbert space topology is used in the completion of the underlying indefinite metric inner product space however it is also found that if the topology is varied with the parameter of the hamiltonian in the manner similar to analytic continuation then the hamiltonian keeps positive integer eigenvalues with a complete set of eigenvectors

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

on the multifractal analysis of bernoulli convolutions i large deviation results we show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved bernoulli measures for the golden mean in this first part we establish some large deviation results for random products of matrices using perturbation theory of quasicompact operators

deterministic blind modulation induced source separation for digital wireless communications in this paper we present a new simple deterministic blind source separation algorithm which is based on modulating the same data symbol sequence with different code sequences and transmitting the resulting modulated data symbol sequences through different antennas the algorithm does not exploit the finite alphabet property of the data symbols as a result no iterations are required and convergence is not an issue instantaneous mixtures frequency flat fading as well as convolutive mixtures frequency selective fading can be handled in the case of a convolutive mixture the difficulties that occur when the users have unequal channel orders are avoided moreover the proposed algorithm is robust against channel order underestimation

large deviations for products of random two dimensional matrices we establish large deviation type estimates for i i d products of two dimensional random matrices with finitely supported probability distribution the estimates are stable under perturbations and require no irreducibility assumptions in consequence we obtain a uniform local modulus of continuity for the corresponding lyapunov exponent regarded as a function of the support of the distribution this in turn has consequences on the modulus of continuity of the integrated density of states and on the localization properties of random jacobi operators

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

localization for off diagonal disorder and for continuous schrodinger operators we extend the proof of localization by delyon levy and souillard to accommodate the anderson model with off diagonal disorder and the continuous schrodinger equation with a random potential

central limit theorem in negative curvature we prove a central limit theorem for the distance of the brownian point on the universal cover of a compact negatively curved riemannian manifold the technical point is a contraction property for the leafwise brownian motion along the stable foliation

a supersymmetric generalization of von neumann s theorem a formulation of supersymmetric quantum mechanics is given and superunitary and generalized canonical transformations are defined acting in a module next it is assumed that there are operators that give an irreducible representation of the canonical commutation and anticommutation relations respectively and it is proved that two such representations are connected by a uniquely determined superunitary transformation under suitable domain assumptions this extends the well known uniqueness theorem of von neumann to canonical anti commutation relations using anticommuting parameters

theoremes limite pour les systemes lineaires a coefficients markoviens nous montrons un theoreme central limite et une estimee des grandes deviations pour les solutions d equations differentielles stochastiques lineaires a coefficients markoviens ces resultats sont obtenus dans le cadre general des processus markoviens multiplicatifs ils s appliquent alors par exemple au flot derive d un flot stochastique sur une variete compacte et aux produits de matrices aleatoires en dependance markovienne

a general scheme for equalization of space time block coded systems with unknown csi recently space time block codes stbcs have gained much attention as an effective transmit diversity technique to increase the capacity of wireless communication systems in this paper we consider a general technique for direct equalization of space time block coding systems with unknown channel state information csi this technique is suitable for several existing hybrid stbc schemes such as stbc orthogonal frequency division multiplexing stbc ofdm and stbc code division multiple access stbc cdma we show that by exploiting the redundancy in the structure of stbc a zero forcing equalizer can be constructed without channel estimation the conditions for the identifiability of the zero forcing equalizer are also derived to ensure correct equalization to further improve the performance of the proposed method a new iterative algorithm is developed by incorporating the finite alphabet property of information symbols simulation results show that the proposed algorithms can outperform comparative schemes in most simulation conditions

limit theorems for products of positive random matrices let s be the set of q times q matrices with positive entries such that each column and each row contains a strictly positive element and denote by s circ the subset of these matrices all entries of which are strictly positive consider a random ergodic sequence x n n geq1 in s the aim of this paper is to describe the asymptotic behavior of the random products x n x n ldots x 1 n geq 1 under the main hypothesis p bigcup n geq 1 x n in s circ 0 we first study the behavior in direction of row and column vectors of x n then adding a moment condition we prove a law of large numbers for the entries and lengths of these vectors and also for the spectral radius of x n under the mixing hypotheses that are usual in the case of sums of real random variables we get a central limit theorem for the previous quantities the variance of the gaussian limit law is strictly positive except when x n n geq 1 is tight this tightness property is fully studied when the x n n geq 1 are independent

a semi blind channel estimation method for multiuser multiantenna ofdm systems a subspace based blind method is proposed for estimating the channel responses of a multiuser and multiantenna orthogonal frequency division multiplexing ofdm uplink system it gives estimations to all channel responses subject to a scalar matrix ambiguity and does not need precise channel order information only an upper bound for the orders is required furthermore the scalar ambiguity matrix can be easily resolved by using only one pilot ofdm block given that the number of users is smaller than the number of symbols in the pilot symbol block equalization methods are discussed based on the estimated channels by using partial knowledge of the channels a multipath subspace method is proposed that reduces the computational complexity simulations show that the methods are effective and robust

optimal predictions of powers of conditionally heteroscedastic processes in conditionally heteroskedastic models the optimal prediction of powers or logarithms of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process a standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi maximum likelihood qml in a first step and to use empirical means based on rescaled innovations to estimate the expectation in a second step this paper proposes an alternative one step procedure based on an appropriate non gaussian qml estimation of the model and establishes the asymptotic properties of the two approaches their performances are compared for finite order garch models and for the infinite arch for the standard garch p q and the asymmetric power garch p q it is shown that the are of the estimators only depends on the prediction problem and some moments of the independent process an application to indexes of major stock exchanges is proposed

sign based portmanteau test for arch type models with heavy tailed innovations this paper proposes a sign based portmanteau test for diagnostic checking of arch type models estimated by the least absolute deviation approach under the strict stationarity condition the asymptotic distribution is obtained the new test is applicable for very heavy tailed innovations with only finite fractional moments simulations are undertaken to assess the performance of the sign based test as well as a comparison with other two portmanteau tests a real empirical example for exchange rates is given to illustrate the practical usefulness of the test

asymptotics of cholesky garch models and time varying conditional betas this paper proposes a new model with time varying slope coefficients our model called char is a cholesky garch model based on the cholesky decomposition of the conditional variance matrix introduced by pourahmadi 1999 in the context of longitudinal data we derive stationarity and invertibility conditions and prove consistency and asymptotic normality of the full and equation by equation qml estimators of this model we then show that this class of models is useful to estimate conditional betas and compare it to the approach proposed by engle 2016 finally we use real data in a portfolio and risk management exercise we find that the char model outperforms a model with constant betas as well as the dynamic conditional beta model of engle 2016

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

on certain large random hermitian jacobi matrices with applications to wireless communications in this paper we study the spectrum of certain large random hermitian jacobi matrices these matrices are known to describe certain communication setups in particular we are interested in an uplink cellular channel which models mobile users experiencing a soft handoff situation under joint multicell decoding considering rather general fading statistics we provide a closed form expression for the per cell sum rate of this channel in high signal to noise ratio snr when an intra cell time division multiple access tdma protocol is employed since the matrices of interest are tridiagonal their eigenvectors can be considered as sequences with second order linear recurrence therefore the problem is reduced to the study of the exponential growth of products of two by two matrices for the case where k users are simultaneously active in each cell we obtain a series of lower and upper bound on the high snr power offset of the per cell sum rate which are considerably tighter than previously known bounds

random walks on three strand braids and on related hyperbolic groups we investigate the statistical properties of random walks on the simplest nontrivial braid group b3 and on related hyperbolic groups we provide a method using cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories the drift and the return probability the action of the groups under consideration in the hyperbolic plane is investigated and the distribution of a geometric invariant the hyperbolic distance is analysed it is shown that a random walk on b3 can be viewed as a magnetic random walk on the group psl 2

per tone equalization for mimo ofdm systems this paper focuses on multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems with channel order larger than the cyclic prefix cp length writing the demodulating fast fourier transform fft as a sliding fft followed by a downsampling operation we show in this paper that by swapping the filtering operations of the mimo channel and the sliding fft the data model for the temporally smoothened received signal of each individual tone of the mimo ofdm system is very similar to the data model for the temporally smoothened received signal of a mimo single carrier sc system as a result to recover the data symbol vectors the conventional equalization approach for mimo sc systems can be applied to each individual tone of the mimo ofdm system this so called per tone equalization pteq approach for mimo ofdm systems is an attractive alternative to the recently developed time domain equalization teq approach for mimo ofdm systems in the second part of this paper we focus on direct per tone equalizer design and adapt an existing semi blind equalizer design method for space time block coding stbc sc systems to the corresponding semi blind per tone equalizer design method for stbc ofdm systems

linear canonical supertransformation on a fock superspace a linear canonical supertransformation is implemented by an inner product preserving operator which is necessarily not continuous

common volatility and correlation clustering in asset returns abstract we present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations our approach assumes return innovations with time dependent covariances a cholesky decomposition of the asset covariance matrix with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t as in christodoulakis and satchell christodoulakis g a satchell s e 2002 correlated arch corrarch modelling the time varying conditional correlation between financial asset returns european journal of operational research 139 2 350 369 correlation is generated by conditionally autoregressive processes thus allowing for an autocorrelation structure for correlation our approach allows for explicit out of sample forecasting and is consistent with stylized facts as time varying correlations and correlation clustering co movement between correlation coefficients correlation and volatility as well as between volatility processes co volatility the latter two are shown to depend on correlation and volatility persistence empirical evidence on a trivariate model using monthly data from dow jones industrial nasdaq composite and the 3 month us treasury bill yield supports our theoretical arguments

lie groups and lie algebras with generalized supersymmetric parameters matrices with symmetric parameters the most general extension of supersymmetric parameters are investigated the superdeterminants of such matrices are defined lie groups consisting of these matrices and their lie algebras are studied

on the multifractal analysis of bernoulli convolutions ii dimensions we show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved bernoulli measures for the golden mean in this second part we show how the hausdorff dimension of the set where the measure has a power law singularity of strength is related to the large deviation function given in part i

convergence in distribution of products of random matrices we consider a sequence a2 a2 of i i d nonnegative matrices of size d d and investigate convergence in distribution of the product mn a1 an when d 2 it is possible for mn to converge in distribution without normalization to a distribution not concentrated on the zero matrix several equivalent conditions for this to happen are given these lead to a fairly general family of examples these conditions can also be used to determine when the a s limit of 1 nlog mn equals the logarithm of the largest eigenvalue of e a1

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

global self weighted and local quasi maximum exponential likelihood estimators for arma garch igarch models this paper investigates the asymptotic theory of the quasi maximum exponential likelihood estimators qmele for arma garch models under only a fractional moment condition the strong consistency and the asymptotic normality of the global self weighted qmele are obtained based on this self weighted qmele the local qmele is showed to be asymptotically normal for the arma model with garch finite variance and igarch errors a formal comparison of two estimators is given for some cases a simulation study is carried out to assess the performance of these estimators and a real example on the world crude oil price is given

recurrent random walks in nonnegative matrices attractors of certain iterated function systems in this paper the structure of the set of recurrent points for random walks in finite dimensional nonnegative matrices is determined the structural results are then used in understanding attractors of certain not necessarily contractive iterated function systems