bit interleaved coded modulation with iterative decoding and 8 psk signaling we have suggested bit interleaved coded modulation with soft decision iterative decoding bicm id for bandwidth efficient transmission over gaussian and fading channels unlike trellis coded modulation bicm id has a small free euclidean distance but large diversity order due to bit interleaving with iterative decoding soft bit decisions can be employed to significantly improve the conditional intersignal euclidean distance this leads to a large coding gain comparable to that of turbo tcm over both gaussian and rayleigh fading channels with much less system complexity we address critical design issues to enhance the decoding performance and provide the analytical bounds on the performance with an ideal feedback assumption we investigate the performance characteristics of bicm id through extensive simulations and show that at high signal to noise ratios the performance of bicm id converges to the performance assuming error free feedback

frechet differentiability for a damped sine gordon equation abstract we consider a damped sine gordon equation with a variable diffusion coefficient the goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function j first we show that the solution map is continuous under a weak assumption on the topology of the admissible set p then the solution map is shown to be weakly g teux differentiable on p implying the g teux differentiability of the objective function finally we show the frechet differentiability of j the optimal set of parameters is shown to satisfy a bang bang control law

hausdorff moment problem and fractional moments a simplified procedure abstract the purpose of this paper is the recovering of a probability density function with support 0 1 from the knowledge of its sequence of moments i e the classical hausdorff moment problem to avoid the well known ill conditioning firstly the moment curve is calculated from the assigned sequence of moments next the unknown density is approximated by maximum entropy maxent technique selecting some proper points on the moment curve exploiting convergence in entropy a simplified quick procedure is suggested to recover the approximate density an application to laplace transform inversion is illustrated

global wave front sets of banach frechet and modulation spacetypes and pseudo differential operators we introduce global wave front sets with respect to suitable banach or frechet spaces an important special case appears when choosing these spaces as modulation spaces we show that the standard p

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

option pricing for a large trader with price impact and liquidity costs abstract this paper concerns the pricing of options for a large trader in a market with liquidity risk the investor s trading action is assumed to have some lasting impact on the underlying asset and the effect of illiquidity is modeled via trading speed rate of change in holdings for such a large trader liquidity risk is quite important since the permanent price impact as well as liquidity costs incurred during trading must be taken into account the utility maximization approach to determine option prices leads to optimal control problems this paper shows that the value functions of these optimal control problems are the unique viscosity solutions of a fully nonlinear second order pde moreover some illustrative examples with explicit optimal solutions and numerical results are presented

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

quadratures and integral transforms arising from generating functions abstract by using the explicit form of the eigenvectors of the finite jacobi matrix associated to a family of orthogonal polynomials and some asymptotic expressions we obtain quadrature formulas for the integral transforms arising from linear generating functions of the classical orthogonal polynomials as a bypass product we obtain simple and accurate riemann steklov quadrature formulas and as an application of this quadrature formalism we obtain the relationship between the fractional fourier transform and the canonical coherent states

spectral clustering properties of block multilevel hankel matrices abstract by means of recent results concerning spectral distributions of toeplitz matrices we show that the singular values of a sequence of block p level hankel matrices h n generated by a p variate matrix valued measure whose singular part is finitely supported are always clustered at zero thus extending a result known when p 1 and is real valued and lipschitz continuous the theorems hold for both eigenvalues and singular values in the case of singular values we allow the involved matrices to be rectangular

approximation of probability density functions by the multilevel monte carlo maximum entropy method we develop a complete convergence theory for the maximum entropy method based on moment matching for a sequence of approximate statistical moments estimated by the multilevel monte carlo method under appropriate regularity assumptions on the target probability density function the proposed method is superior to the maximum entropy method with moments estimated by the monte carlo method new theoretical results are illustrated in numerical examples

spectral properties of hankel matrices and numerical solutions of finite moment problems abstract after proving that any hankel matrix generated by moments of positive functions is conditioned essentially the same as the hilbert matrix of the same size we show a preconditioning technique i e a congruence transform of the original hankel matrix that drastically reduces its ill conditioning applications of this result to classical orthogonal polynomial sequences and to modified moment problems are given also we outline an efficient algorithm for the computation of the function f x w x exp p x where w x is positive and p x is a polynomial of degree n 1 from the knowledge of its first n moments

universal decoding for frequency selective fading channels we address the problem of universal decoding in unknown frequency selective fading channels using an orthogonal frequency division multiplexing ofdm signaling scheme a block fading model is adopted where the bands fading coefficients are unknown yet assumed constant throughout the block given a codebook we seek a decoder independent of the channel parameters whose worst case performance relative to a maximum likelihood ml decoder that knows the channel is optimal specifically the decoder is selected from a family of quadratic decoders and the optimal decoder is referred to as a quadratic minimax qmm decoder for that family as the qmm decoder is generally difficult to find a suboptimal qmm decoder is derived instead despite its suboptimality the proposed decoder is shown to outperform the generalized likelihood ratio test glrt which is commonly used when the channel is unknown while maintaining a comparable complexity the qmm decoder is also derived for the practical case where the fading coefficients are not entirely independent but rather satisfy some general constraints simulations verify the superiority of the proposed qmm decoder over the glrt and over the practically used training sequence approach

efficient evaluation of the pdf of a random variable through the kernel density maximum entropy approach in this paper a new approach for the evaluation of the probability density function pdf of a random variable from the knowledge of its lower moments is presented at first the classical moment problem mp is revisited which gives the conditions such that the assigned sequence of sample moments represent really a sequence of moments of any distribution then an alternative approach is presented termed as the kernel density maximum entropy maxent method by the authors which approximates the target pdf as a convex linear combination of kernel densities transforming the original mp into a discrete mp which is solved through a maxent approach in this way simply solving a discrete maxent problem not requiring the evaluation of numerical integrals an approximating pdf converging toward the maxent pdf is obtained the method is first demonstrated by approximating some known analytical pdfs the chi square and the gumbel pdfs and then it is applied to some experimental engineering problems namely for modelling the pdf of concrete strength the circular frequency and the damping ratio of strong ground motions the extreme wind speed in messina s strait region all the developed numerical applications show the goodness and efficacy of the proposed procedure copyright 2008 john wiley sons ltd

on the numerical solution of nonlinear option pricing equation in illiquid markets abstract in this paper we focus on the numerical solution of nonlinear black scholes equation modeling illiquid markets two monotone unconditionally stable splitting methods ensuring positive numerical solution and avoiding unstable oscillations are applied to solve nonlinear black scholes equation modeling illiquid markets these numerical methods are based on the lod methods which allow us to solve the discrete equation explicitly the properties of these methods are analyzed the numerical results for vanilla call option are compared to the local crank nicolson scheme the numerical results for european butterfly spread are also provided

laplace transform inversion on the real line is truly ill conditioned in this note we consider laplace transforms of probability distribution functions f t on 0 that have finite integer moments of all orders we construct a family f w t of distribution functions whose laplace transforms differ from that of f t by as little as we want but such that f w t has a discrete part whereas f t has a density f t thus we provide one more example of why laplace transform inversion on the real line is a difficult ill conditioned inverse problem

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

the complexity of minimal degenerations for representation finite selfinjective algebras abstract minimal degenerations of modules over all but one exceptional class of representation finite selfinjective algebras are given by extensions g zwara colloq math 75 1998 91 this means in terms of the complexity of degenerations that these minimal degenerations have complexity one the minimal degenerations of modules for the exceptional class of representation finite selfinjective algebras are studied by r aehle j london math soc 66 2002 73 in this paper it is shown that these degenerations have complexity less or equal to two

on the numerical solution of nonlinear black scholes equations nonlinear black scholes equations have been increasingly attracting interest over the last two decades since they provide more accurate values by taking into account more realistic assumptions such as transaction costs risks from an unprotected portfolio large investor s preferences or illiquid markets which may have an impact on the stock price the volatility the drift and the option price itself in this paper we will focus on several models from the most relevant class of nonlinear black scholes equations for european and american options with a volatility depending on different factors such as the stock price the time the option price and its derivatives due to transaction costs we will analytically approach the option price by transforming the problem for a european call option into a convection diffusion equation with a nonlinear term and the free boundary problem for an american call option into a fully nonlinear nonlocal parabolic equation defined on a fixed domain following sevcovic s idea finally we will present the results of different numerical discretization schemes for european options for various volatility models including the leland model the barles and soner model and the risk adjusted pricing methodology model

how bad are hankel matrices considered are hankel vandermonde and krylov basis matrices it is proved that for any real positive definite hankel matrix of order n its spectral condition number is bounded from below by 3 cdot 2 n 6 also proved is that the spectral condition number of a krylov basis matrix is bounded from below by 3 frac 1 2 cdot 2 frac n 2 3 for v v x 1 ldots x n a vandermonde matrix with arbitrary but pairwise distinct nodes x 1 ldots x n we show that mbox rm cond 2 v geq 2 n 2 n frac 1 2 if either x j leq 1 or x j geq 1 for all j then mbox rm cond 2 v geq 2 n 2

on degenerations and extensions of finite dimensional modules abstract we derive a cancellation theorem for degenerations of modules that says in particular that projective or injective common direct summands can always be neglected combining the cancellation result with the existence of almost split sequences we characterize the orbit closure of a module living on preprojective components by the fact that the dimension of the homomorphism space to any other module does not decrease for representation directed algebras whence in particular for path algebras of dynkin quivers we provide an alternative proof which shows in addition that any minimal degenerationnofmcomes from an exact sequence with middle termmwhose end terms add up ton by a careful examination the same is true for degenerations of matrix pencils having used so far the existence of certain extensions to obtain degenerations we then turn the tables and use degenerations to produce a lot of interesting short exact sequences in particular we show that any non simple indecomposable over a tame quiver is an extension of an indecomposable and a simple

algebraic description of the finite stieltjes moment problem abstract the stieltjes problem of moments seeks for a nondecreasing positive distribution function on the semi axis 0 so that its moments match a given infinite sequence of positive real numbers m 0 m 1 in his seminal paper investigations on continued fractions published in 1894 stieltjes gave a complete solution including the conditions for the existence and uniqueness in relation to his main goal the convergence theory of continued fractions one can also reformulate the stieltjes problem of moments as looking for a sequence of positive distribution functions 1 2 where the nth distribution function has n points of increase and m 0 m 1 m 2 n 1 represent its first 2n moments i e as the sequence of the finite stieltjes moment problems this view can be linked to iterative solution of large linear algebraic systems providing that m 0 m 1 are moments of some linear self adjoint and coercive operator a on a hilbert space with respect to a given vector f the finite stieltjes moment problems determine the iterations of the conjugate gradient method applied for solving a u f and vice versa here the existence and uniqueness is guaranteed by the properties of the operator a reformulation for finite sequences matrices and finite vectors is obvious this fundamental link raises a question on how the solution of the finite stieltjes moment problem can be described purely algebraically this has motivated the presented exposition built upon ideas published previously by several authors since the description uses matrices of moments it is not intended for numerical computations

hausdorff moment problem via fractional moments we outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments the approximate density is obtained resorting to maximum entropy technique under the constraint of some fractional moments the latter ones are obtained explicitly in terms of the infinite sequence of given ordinary moments it is proved that the approximate density converges in entropy to underlying density so that it turns out to be useful for calculating expected values

numerical aspects of finite hausdorff moment problem by maximum entropy approach some numerical aspects of the finite hausdorff moment problem in the framework of maximum entropy have been reviewed as stability of lagrange s multipliers computation entropy decreasing averages estimate spectral properties of hankel matrices have been considered determinant and conditioning number have been estimated finally entropy estimate has been provided

born expansion and frechet derivatives in nonlinear diffuse optical tomography the nonlinear diffuse optical tomography dot problem involves the inversion of the associated coefficient to measurement operator which maps the spatially varying optical coefficients of turbid medium to the boundary measurements the inversion of the coefficient to measurement operator is approximated by using the frechet derivative of the operator in this work we first analyze the born expansion show the conditions which ensure the existence and convergence of the born expansion and compute the error in the mth order born approximation then we derive the mth order frechet derivatives of the coefficient to measurement operator using the relationship between the frechet derivatives and the born expansion

moment information and entropy evaluation for probability densities abstract how much information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution we prove that a reliable evaluation of the corresponding shannon entropy can be done by exploiting some known theoretical results on the entropy convergence uniquely involving exact moments without solving the underlying moment problem all the procedure essentially rests on the solution of linear systems with nearly singular matrices and hence it requires both calculations in high precision and a pre conditioning technique numerical examples are provided to support the theoretical results

on convergence of the modified newton s method under holder continuous frechet derivative in this paper the upper and lower estimates of the radius of the convergence ball of the modified newton s method in banach space are provided under the hypotheses that the frechet derivative of the nonlinear operator are center holder continuous for the initial point and the solution of the operator the error analysis is given which matches the convergence order of the modified newton s method the uniqueness ball of solution is also established numerical examples for validating the results are also provided including a two point boundary value problem

bayesian equalization for ldpc channel decoding we describe the channel equalization problem and its prior estimate of the channel state information csi as a joint bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder our approach takes into consideration not only the uncertainty due to the noise in the channel but also the uncertainty in the csi estimate however this solution cannot be computed in linear time because it depends on all the transmitted symbols hence we also put forward an approximation for each symbol s posterior using the expectation propagation algorithm which is optimal from the kullback leibler divergence viewpoint and yields an equalization with a complexity identical to the bcjr algorithm we also use a graphical model representation of the full posterior in which the proposed approximation can be readily understood the proposed posterior estimates are more accurate than those computed using the ml estimate for the csi in order to illustrate this point we measure the error rate at the output of a low density parity check decoder which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates for example for qpsk modulation and a channel with three taps we can expect gains over 0 5 db with same computational complexity as the ml receiver

on the outage capacity of a practical decoder accounting for channel estimation inaccuracies the optimal decoder achieving the outage capacity under imperfect channel estimation is investigated first by searching into the family of nearest neighbor decoders which can be easily implemented on most practical coded modulation systems we derive a decoding metric that minimizes the average of the transmission error probability over all channel estimation errors next we specialize our general expression to obtain the corresponding decoding metric for fading mimo channels according to the notion of estimation induced outage eio capacity introduced in our previous work and assuming a block rayleigh fading channel we characterize the maximal achievable information rates using gaussian codebooks associated to the proposed decoder these achievable rates are compared to the rates achieved by the classical mismatched maximum likelihood ml decoder and the ultimate limits given by the eio capacity numerical results show that the derived metric provides significant gains in terms of achievable eio rates and bit error rate ber in a bit interleaved coded modulation bicm framework without introducing any additional decoding complexity however the achievable rates of such metric are still far from the eio capacity

gaussian codes and weighted nearest neighbor decoding in fading multiple antenna channels we investigate the fading multiple antenna channel the decoder is assumed to possess imperfect channel fading information a modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information gmi the achievable rate is obtained we show that under certain conditions the achievable rate is equivalent to that of a fading multiple antenna gaussian channel where fading is known to the receiver and is equal to the channel estimation and where noise is due to both the channel noise and the channel estimation error we show that for our communication scheme the minimum mean square error mmse channel estimator is optimal in the sense that it achieves the highest value of gmi and hence the highest communication rate additionally a training based multiple input multiple output mimo scheme in a block fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal to noise ratio snr

an upwind finite difference method for a nonlinear black scholes equation governing european option valuation under transaction costs in this paper we develop a numerical method for a nonlinear parabolic partial differential equation arising from pricing european options under transaction costs the method is based on an upwind finite difference scheme for the spatial discretization and a fully implicit time stepping scheme we prove that the system matrix from this scheme is an m matrix and that the approximate solution converges unconditionally to the viscosity solution to the equation by showing that the scheme is consistent monotone and unconditionally stable a newton iterative algorithm is proposed for solving the discretized nonlinear system of which the jacobian matrix is shown to be also an m matrix numerical experiments are performed to demonstrate the accuracy and robustness of the method

a backprojection algorithm for electrical impedance imaging the authors study a two dimensional reconstruction algorithm due to d c barber and b h brown applied to a linearized electrostatic inverse problem first the authors demonstrate how this algorithm fits within the framework of inverses of generalized radon transforms studied by g beylkin second an iterative improvement of the barber brown algorithm is constructed based on the conjugate residual method several numerical results obtained with this iterative algorithm are presented

the hausdorff entropic moment problem our aim in this paper is twofold first to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers n n 0 to represent the entropic moments 0 a x ndx of an unknown non negative decreasing and differentiable a e density function x with a finite interval support these moments are called entropic moments because they are closely connected with various information entropies renyi tsallis second we outline an efficient method for the reconstruction of the density function from the knowledge of its first n entropic moments

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

numerical solution of linear and nonlinear black scholes option pricing equations this paper deals with the numerical solution of black scholes option pricing partial differential equations by means of semidiscretization technique for the linear case a fourth order discretization with respect to the underlying asset variable allows a highly accurate approximation of the solution for the nonlinear case of interest modeling option pricing with transaction costs semidiscretization technique provides a competitive numerical solution with respect to others recently given in b during m fournier a jungel convergence of a high order compact finite difference scheme for a nonlinear black scholes equation esaim math modelling numer anal modelisation mathematique et analyse numerique 38 2004 359 369 b during black scholes type equations mathematical analysis parameter identification numerical solution dissertation university mainz july 2005

numerical inversion of the laplace transform and its application to fractional diffusion abstract a procedure for computing the inverse laplace transform of real data is obtained by using a bessel type quadrature which is given in terms of laguerre polynomials l n x and their zeros this quadrature yields a very simple matrix expression for the laplace transform g s of a function f t which can be inverted for real values of s we show in this paper that the inherent instability of this inversion formula can be controlled by selecting a proper set of the parameters involved in the procedure instead of using standard regularization methods we demonstrate how this inversion method is particularly well suited to solve problems of the form l 1 s g s t f t f 0 t as an application of this procedure numerical solutions of a fractional differential equation modeling subdiffusion are obtained and a mean square displacement law is numerically found

a numerical method for pricing discrete double barrier option by legendre multiwavelet in this article a fast numerical algorithm for pricing discrete double barrier option is presented according to blackscholes model the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution these recursive solutions are approximated by using legendre multiwavelets as orthonormal basis functions and expressed in operational matrix form the most important feature of this method is that its cpu time is nearly invariant when monitoring dates increase besides the rate of convergence of presented algorithm was obtained the numerical results verify the validity and efficiency of the numerical method

laplace transform and finite difference methods for the black scholes equation in this paper we explore discrete monitored barrier options in the black scholes framework the discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volatility is assumed here a technique mixing the laplace transform and the finite difference method to solve black scholes pde is considered equivalence between the post widder inversion formula joint with finite difference and the standard finite difference technique is proved the mixed method is positivity preserving satisfies the discrete maximum principle according to financial meaning of the involved pde and converges to the underlying solution in presence of low volatility equivalence between methods allows some physical interpretations

moment closure approximations of the boltzmann equation based on varphi divergences this paper is concerned with approximations of the boltzmann equation based on the method of moments we propose a generalization of the setting of the moment closure problem from relative entropy to varphi divergences and a corresponding closure procedure based on minimization of varphi divergences the proposed description encapsulates as special cases grad s classical closure based on expansion in hermite polynomials and levermore s entropy based closure we establish that the generalization to divergence based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment closure formulations such as inadmissibility of the approximate phase space distribution potential loss of hyperbolicity and singularity of flux functions at local equilibrium the divergence based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the boltzmann equation

entropy and density approximation from laplace transforms how much information does the laplace transforms on the real line carry about an unknown absolutely continuous distribution if we measure that information by the boltzmann gibbs shannon entropy the original question becomes how to determine the information in a probability density from the given values of its laplace transform we prove that a reliable evaluation both of the entropy and density can be done by exploiting some theoretical results about entropy convergence that involve only finitely many real values of the laplace transform without having to invert the laplace transform we provide a bound for the approximation error of in terms of the kullback leibler distance and a method for calculating the density to arbitrary accuracy

the bad truth about laplace s transform inverting the laplace transform is a paradigm for exponentially ill posed problems for a class of operators including the laplace transform we give forward and inverse formulae that have fast implementations using the fast fourier transform these formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the laplace transform