parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

generalized covariations local time and stratonovich ito s formula for fractional brownian motion with hurst index h 1 4 given a locally bounded real function g we examine the existence of a 4 covariation g b h b h b h b h where b h is a fractional brownian motion with a hurst index h ge tfrac 1 4 we provide two essential applications first we relate the 4 covariation to one expression involving the derivative of local time in the case h tfrac 1 4 generalizing an identity of bouleau yor type well known for the classical brownian motion a second application is an ito formula of stratonovich type for f b h the main difficulty comes from the fact b h has only a finite 4 variation

forward backward and symmetric stochastic integration we define three types of non causal stochastic integrals forward backward and symmetric our approach consists in approximating the integrator two optics are considered the first one is based on traditional usual stochastic calculus and the second one on wiener distributions

on conformal powers of the dirac operator on einstein manifolds we determine the structure of conformal powers of the dirac operator on einstein spin manifolds in terms of the product formula for shifted dirac operators the result is based on the techniques of higher variations for the dirac operator on einstein manifolds and spectral analysis of the dirac operator on the associated poincare einstein metric and relies on combinatorial recurrence identities related to the dual hahn polynomials

integration by parts and time reversal for diffusion processes in this paper we obtain necessary and sufficient conditions for the reversibility of the diffusion property assuming the existence of a density at every time t the proofs are based on techniques of the stochastic calculus of variations

integration with respect to the g brownian local time abstract let l be the local time of g brownian motion b in this paper we consider the existence of the quadratic covariation f b b t and the integral r f x l d x t under some suitable conditions we show that the sublinear version of the bouleau yor identity r f x l d x t f b b t holds these allow us to write the ito formula for c 1 functions

a new conformal invariant on 3 dimensional manifolds abstract by improving the analysis developed in the study of k yamabe problem we prove in this paper the following new inequality for any 3 dimensional riemannian manifold m 3 g of non negative scalar curvature m 1 g d v g 2 3 vol g m 2 g d v g equality holds if and only if m 3 g is a space form

a fast algorithm for maximum likelihood estimation of harmonic chirp parameters the analysis of approximately periodic signals is an important element in numerous applications one generalization of standard periodic signals often occurring in practice is harmonic chirp signals where the instantaneous frequency increases decreases linearly as a function of time a statistically efficient estimator for extracting the parameters of the harmonic chirp model in additive white gaussian noise is the maximum likelihood ml estimator which recently has been demonstrated to be robust to noise and accurate even when the model order is unknown the main drawback of the ml estimator is that only very computationally demanding algorithms for computing an estimate are known in this paper we give an algorithm for computing an estimate to the ml estimator for a number of candidate model orders with a much lower computational complexity than previously reported in the literature the lower computational complexity is achieved by exploiting recursive matrix structures including a block toeplitz plus hankel structure the fast fourier transform and using a two step approach composed of a grid and refinement step to reduce the number of required function evaluations the proposed algorithms are assessed via monte carlo and timing studies the timing studies show that the proposed algorithm is orders of magnitude faster than a recently proposed algorithm for practical sizes of the number of harmonics and the length of the signal

tractor calculi for parabolic geometries parabolic geometries may be considered as curved analogues of the homogeneous spaces g p where g is a semisimple lie group and p c g a parabolic subgroup conformal geometries and cr geometries are examples of such structures we present a uniform description of a calculus called tractor calculus based on natural bundles with canonical linear connections for all parabolic geometries it is shown that from these bundles and connections one can recover the cartan bundle and the cartan connection in particular we characterize the normal cartan connection from this induced bundle connection perspective we construct explicitly a family of fundamental first order differential operators which are analogous to a covariant derivative iterable and defined on all natural vector bundles on parabolic geometries for an important subclass of parabolic geometries we explicitly and directly construct the tractor bundles their canonical linear connections and the machinery for explicitly calculating via the tractor calculus

branching laws for verma modules and applications in parabolic geometry i abstract we initiate a new study of differential operators with symmetries and combine this with the study of branching laws for verma modules of reductive lie algebras by the criterion for discretely decomposable and multiplicity free restrictions of generalized verma modules t kobayashi 2012 22 we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds then we apply a new method f method relying on the fourier transform to find singular vectors in generalized verma modules which significantly simplifies and generalizes many preceding works in certain cases it also determines the jordan holder series of the restriction for singular parameters the f method yields an explicit formula of such unique operators for example giving an intrinsic and new proof of juhl s conformally invariant differential operators juhl 2009 16 and its generalizations to spinor bundles this article is the first in the series and the next ones include their extension to curved cases together with more applications of the f method to various settings in parabolic geometries

estimates and extremals for zeta function determinants on four manifolds leta be a positive integral power of a natural conformally covariant differential operator on tensor spinors in a riemannian manifold suppose thata is formally self adjoint and has positive definite leading symbol for example a could be the conformal laplacian yamabe operator l or the square of the dirac operator open image in new window within the conformal class left g e 2w g 0 w in c infty m right of an einstein locally symmetric background metricgo on a compact four manifoldm we use an exponential sobolev inequality of adams to show that bounds on the functional determinant ofa and the volume ofg imply bounds on thew2 2 norm of the conformal factorw provided that a certain conformally invariant geometric constantk k m g o a is strictly less than 32 2 we show for the operatorsl and open image in new window that indeedk 32 2 except when m g o is the standard sphere or a hyperbolic space form on the sphere a centering argument allows us to obtain a bound of the same type despite the fact thatk is exactly equal to 32 2 in this case finally we use an inequality of beckner to show that in the conformal class of the standard four sphere the determinant ofl or of open image in new window is extremized exactly at the standard metric and its images under the conformal transformation groupo 5 1

einstein and conformally flat critical metrics of the volume functional let r be a constant let m r be the space of smooth metrics g on a given compact manifold n n 3 with smooth boundary such that g has constant scalar curvature r and g is a fixed metric on let v g be the volume of g m r in this work we classify all einstein or conformally flat metrics which are critical points of v in m r

a variational approach to the construction and malliavin differentiability of strong solutions of sde s in this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients we aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by brownian motion an important and rather surprising consequence of our method which is based on malliavin calculus is that the solutions derived by veretennikov theory probab appl 24 354 366 1979 for brownian motion with bounded and measurable drift in mathbb r d are malliavin differentiable further a strength of our approach which does not rely on a pathwise uniqueness argument is that it can be transferred and applied to the analysis of various other types of stochastic equations we obtain a bismut elworthy li formula elworthy and li j funct anal 125 252 286 1994 for spatial derivatives of solutions to the kolmogorov equation with bounded and measurable drift coefficients to derive the formula we use that our approach can be applied to obtain sobolev differentiability in the initial condition in addition to malliavin differentiability of the associated stochastic differential equations another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields moreover our approach is also applicable to the construction of solutions of stochastic evolution equations on hilbert spaces

maximum likelihood parameter estimation of superimposed chirps using monte carlo importance sampling we address the problem of parameter estimation of superimposed chirp signals in noise the approach used here is a computationally modest implementation of a maximum likelihood ml technique the ml technique for estimating the complex amplitudes chirping rates and frequencies reduces to a separable optimization problem where the chirping rates and frequencies are determined by maximizing a compressed likelihood function that is a function of only the chirping rates and frequencies since the compressed likelihood function is multidimensional its maximization via a grid search is impractical we propose a noniterative maximization of the compressed likelihood function using importance sampling simulation results are presented for a scenario involving closely spaced parameters for the individual signals

conformally invariant powers of the laplacian q curvature and tractor calculus we describe an elementary algorithm for expressing as explicit formulae in tractor calculus the conformally invariant gjms operators due to c r graham et alia these differential operators have leading part a power of the laplacian conformal tractor calculus is the natural induced bundle calculus associated to the conformal cartan connection applications discussed include standard formulae for these operators in terms of the levi civita connection and its curvature and a direct definition and formula for t branson s so called q curvature which integrates to a global conformal invariant as well as generalisations of the operators and the q curvature among examples the operators of order 4 6 and 8 and the related q curvatures are treated explicitly the algorithm exploits the ambient metric construction of fefferman and graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions this is partly based on 12 where the relationship of the normal standard tractor bundle to the ambient construction is described

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

conformally invariant powers of the laplacian a complete nonexistence theorem conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo riemannian riemannian conformai and related structures this observation dates back to at least the very early part of the last century when it was shown that the equations of massless particles on curved space time exhibit conformai invariance in this setting a key operator is the con formally invariant wave operator which has leading term a pseudo laplacian the riemannian signature variant of this operator is a fundamental tool in the yam abe problem on compact manifolds here one seeks to find a metric from a given conformai class that has constant scalar curvature recently it has become clear that higher order analogues of these operators viz conformally invariant operators on weighted functions i e conformai densities with leading term a power of the laplacian have a central role in generating and solving other curvature prescription problems as well as other problems in geometric spectral theory and mathematical physics 2 5 15 in the flat setting the existence of such operators dates back to 16 where it is shown that on 4 dimensional minkowski space for k g n 1 2 the kth power of the flat wave operator ak acting on densities of the appropriate weight is invariant under the action of the conformai group more generally if w denotes the space of conformai densities of weight uigl then on a flat conformai manifold of dimension n 3 and any signature there exists for each k e n a unique conformally invariant operator

generalized integration and stochastic odes stochastic forward integrals for processes more general than semimartingales are shown to exist generalized forms of ito wentzell formula and covariation formula are proved and one dimensional stochastic equations driven by finite quadratic variation processes and semimartingales are solved this generalized stochastic calculus is motivated by applications to uniqueness and dependence on parameters for stochastic equations with nonregular drift

scalar curvature deformation and a gluing construction for the einstein constraint equations on a compact manifold the scalar curvature map at generic metrics is a local surjection f m we show that this result may be localized to compact subdomains in an arbitrary riemannian manifold the method is extended to establish the existence of asymptotically flat scalar flat metrics on n n 3 which are spherically symmetric hence schwarzschild at infinity i e outside a compact set such metrics provide cauchy data for the einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically schwarzschild near spatial infinity

extended obstruction tensors and renormalized volume coefficients abstract the behavior is investigated of the renormalized volume coefficients associated to a pseudo riemannian metric under conformal change of the metric it is shown that the renormalized volume coefficients define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of extended obstruction tensors these together with the schouten tensor constitute building blocks for the coefficients in the ambient metric expansion the renormalized volume coefficients have recently been considered by chang and fang motivated by comparison with the elementary symmetric functions of the eigenvalues of the schouten tensor

ito formula for c 1 functions of semimartingales we establish an ito formula forc1 functions of processes whose time reversal are semimartingales and forc1 functions whose first derivatives are holder continuous of any parameter and the process comes out from a stochastic flow of homeomorphism

a new flexible approach to estimate the ia and if of nonstationary signals of long time duration in this paper we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long time duration we locally apply to short time duration intervals the strategy developed in our previous work about nonstationary short time signals this paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low order polynomials parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique the signal is then reconstructed by merging the estimated segments the strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high order polynomial phase signals the estimation of a high order model is not necessary the error propagation phenomenon occurring with the known approach the higher ambiguity function haf based method is avoided the proposed strategy is evaluated using monte carlo noise simulations and compared with the cramer rao bounds crbs the signal of a songbird is used as a real example of its applicability

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

deformation of scalar curvature and volume the stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the einstein metrics one may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant in this paper we localize a condition satisfied by such stationary points to smooth bounded domains the condition involves a generalization of the static equations and we interpret solutions and their boundary values of this equation variationally on domains carrying a metric that does not satisfy the condition we establish a local deformation theorem that allows one to achieve simultaneously small prescribed changes of the scalar curvature and of the volume by a compactly supported variation of the metric we apply this result to obtain a localized gluing theorem for constant scalar curvature metrics in which the total volume is preserved finally we note that starting from a counterexample of min oo s conjecture such as that of brendle marques neves counterexamples of arbitrarily large volume and different topological types can be constructed

variation of total q prime curvature on cr manifolds abstract we derive variational formulas for the total q prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold we also show that the total q prime curvature agrees with the renormalized volume of such domains with respect to the complete kahler einstein metric

mean likelihood frequency estimation estimation of signals with nonlinear as well as linear parameters in noise is studied maximum likelihood estimation has been shown to perform the best among all the methods in such problems joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem where first the nonlinear parameters are estimated via a grid search and then the nonlinear parameter estimates are used to estimate the linear parameters we show that a grid search can be avoided by using the mean likelihood estimator for estimating the unknown nonlinear parameters and how its performance can be made equivalent to that of the maximum likelihood estimator mle the mean likelihood estimator requires computation of a multidimensional integral however using the concepts of importance sampling we obtain the mean likelihood estimate without using integration the technique is computationally far less burdensome than the direct maximum likelihood method but performs just as well simulation examples for estimating frequencies of multiple sinusoids in noise are given the general technique can be applied to a large class of nonlinear regression problems

stochastic systems with memory and jumps abstract stochastic systems with memory naturally appear in life science economy and finance we take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps our results concern existence and uniqueness of strong solutions estimates for the moments and the fundamental tools of calculus such as the ito formula we study the robustness of the solution to the change of noises specifically we consider the noises with infinite activity jumps versus an adequately corrected gaussian noise the study is presented in two different frameworks we work with random variables in infinite dimensions where the values are considered either in an appropriate l p type space or in the space of cadlag paths the choice of the value space is crucial from the modelling point of view as the different settings allow for the treatment of different models of memory or delay our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation

semiholonomic verma modules abstract verma modules arise geometrically through the jets of homogeneous vector bundles we consider in this article the modules that arise from the semiholonomic jets of a homogeneous vector bundle we are particularly concerned with the case of a sphere under mobius transformations in this case there are immediate applications in the theory of conformally invariant differential operators

laplacian operators and q curvature on conformally einstein manifolds a new definition of canonical conformal differential operators p k k 1 2 with leading term a kth power of the laplacian is given for conformally einstein manifolds of any signature these act between density bundles and more generally between weighted tractor bundles of any rank by construction these factor into a power of a fundamental laplacian associated to einstein metrics there are natural conformal laplacian operators on density bundles due to graham jenne mason sparling gjms it is shown that on conformally einstein manifolds these agree with the p k operators and hence on einstein manifolds the gjms operators factor into a product of second order laplacian type operators in even dimension n the gjms operators are defined only for 1 k n 2 and so on conformally einstein manifolds the p k give an extension of this family of operators to operators of all even orders for n even and k n 2 the operators p k are each given by a natural formula in terms of an einstein metric but they are not natural conformally invariant operators in the usual sense they are shown to be nevertheless canonical objects on conformally einstein structures there are generalisations of these results to operators between weighted tractor bundles it is shown that on einstein manifolds the branson q curvature is constant and an explicit formula for the constant is given in terms of the scalar curvature as part of development conformally invariant tractor equations equivalent to the conformal killing equation are presented

estimation of frequency for am fm models using the phase vocoder framework this paper proposes an extension of the applicability of phase vocoder based frequency estimators for generalized sinusoidal models which include phase and amplitude modulations a first approach called phase corrected vocoder pcv takes into account the modification of the fourier phases resulting from these modulations another approach is based on an adaptation of the principles of the time frequency reassignment and is referred to as the reassigned vocoder rv the robustness of the estimation against noise is studied both theoretically and experimentally and the performance is assessed in comparison with two state of the art algorithms an unmodified version of the reassignment method and a quadratically interpolated fast fourier transform method qifft

non uniqueness results for critical metrics of regularized determinants in four dimensions the regularized determinant of the paneitz operator arises in quantum gravity see connes in noncommutative geometry 1994 iv 4 an explicit formula for the relative determinant of two conformally related metrics was computed by branson in commun math phys 178 301 309 1996 a similar formula holds for cheeger s half torsion which plays a role in self dual field theory see juhl in families of conformally covariant differential operators q curvature and holography progress in mathematics vol 275 2009 and is defined in terms of regularized determinants of the hodge laplacian on p forms p n 2 in this article we show that the corresponding actions are unbounded above and below on any conformal four manifold we also show that the conformal class of the round sphere admits a second solution which is not given by the pull back of the round metric by a conformal map thus violating uniqueness up to gauge equivalence these results differ from the properties of the determinant of the conformal laplacian established in commun math phys 149 241 262 1992 ann math 142 171 212 1995 commun math phys 189 655 665 1997

a fast multiple source detection and localization array signal processing algorithm using the spatial filtering and ml approach we propose a computationally efficient algorithm for detection of multiple signals that also gives a rough estimation of their direction of arrivals doas the narrowband received signals from a uniform linear array are first filtered by a set of orthogonal filters e g by a fast fourier transformation in order to separate the sources into multiple spatial intervals this transformation converts the complicated multihypothesis problem of source detection and localization into multiple binary hypothesis testing problems for an additive white gaussian noise awgn environment the maximum likelihood ml solution of these interrelated tests requires substantially less computational complexity than that of the multihypothesis problem for each spatial interval a binary test detects the presence of a single source and thus gives a rough localization we employ generalized likelihood ratio glr tests as the detection criterion assuming that the number of sources their power and the noise variance are all unknown we also show that the optimal uniformly most powerful invariant umpi detector does not exist however we derive a umpi detector that uses some extra information and as a result provides an upper bound performance for evaluation of any invariant detector simulations illustrate that the proposed noniterative glr test performs efficiently for various number of observed data snapshots and signal to noise ratios snr s and its performance is comparable to the upper bound performance we used the proposed algorithm for the initialization of the iterative implementation of the standard ml localization this combination is a high resolution localization algorithm with a low computational complexity

stochastic equations with delay optimal control via bsdes and regular solutions of hamilton jacobi bellman equations we consider an ito stochastic differential equation with delay driven by brownian motion whose solution by an appropriate reformulation defines a markov process x with values in a space of continuous functions mathbf c with generator mathcal l we then consider a backward stochastic differential equation depending on x with unknown processes y z and we study properties of the resulting system in particular we identify the process z as a deterministic functional of x we next prove that the forward backward system provides a suitable solution to a class of parabolic partial differential equations on the space mathbf c driven by mathcal l and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects we also include applications to optimal stochastic control of differential equation with delay in particular we characterize optimal controls as feedback laws in terms of the process x