new dual type decomposition algorithm for nonconvex separable optimization problems abstract the aim of the paper is to present a new dual type decomposition algorithm for large scale nonconvex optimization problems of general separable structure after reformulation of the augmented lagrange function and introduction of auxiliary variables called approximation points separable local optimization problems are created the lower level of the method consists of a few optimization runs of these problems for subsequently improved approximation points whereas standard updating of lagrange multipliers constitutes the highest level simple rules for adjusting the approximation points and the lagrange multipliers are given and thoroughly analysed applicability conditions and example numerical results indicate that the presented algorithm eliminates to a great extent drawbacks of the previous approaches

a geometrical method for removing edge effects from kernel type nonparametric regression estimators abstract we introduce a simple geometric method for removing edge effects from kernel type nonparametric regression estimators it involves reflecting the data set in two estimated points thereby generating a new data set with three times the range of the original data the usual kernel type estimator may be applied to the new enlarged data set without any danger of edge effects this technique is applicable generally to both regularly spaced and randomly spaced designs and admits a natural analog of leave one out cross validation the new cross validation algorithm may be extended to the very ends of the design interval unlike its more conventional counterpart which must be downweighted at the ends of the interval to avoid edge effects

long time behavior of a stochastic sir model abstract in this paper we analyze long time behavior of densities of the distributions of the solution for a stochastic sir epidemic model we prove that the densities can converge in l 1 to an invariant density or can converge weakly to a singular measure

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

small time heat kernel asymptotics at the sub riemannian cut locus for a sub riemannian manifold provided with a smooth volume we relate the small time asymptotics of the heat kernel at a point y of the cut locus from x with roughly how much y is conjugate to x this is done under the hypothesis that all minimizers connecting x to y are strongly normal i e all pieces of the trajectory are not abnormal our result is a renement of the one of leandre 4t logpt x y d 2 x y for t 0 in which only the leading exponential term is detected our results are obtained by extending an idea of molchanov from the riemannian to the sub riemannian case and some details we get appear to be new even in the riemannian context these results permit us to obtain properties of the sub riemannian distance starting from those of the heat kernel and vice versa for the grushin plane endowed with the euclidean volume we get the expansion pt x y t 5 4 exp d 2 x y 4t where y is reached from a riemannian point x by a minimizing geodesic which is conjugate at y

asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators we consider a model of heat conduction introduced in 6 which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures we study the low temperature asymptotic behavior of the invariant measure we show that in this limit the invariant measure is characterized by a variational principle the main technical ingredients are some control theoretic arguments to extend the freidlin wentzell theory of large deviations to a class of degenerate diffusions

decroissance exponentielle du noyau de la chaleur sur la diagonale i we give examples based upon large deviation s theory where the heat kernel of a degenerate diffusion has an exponential decay over the diagonal using malliavin calculus we give conditions for a more generalized heat kernel to have an exponential decay over the diagonal we give lower bound in some particular case by using the bismut s condition

flots et series de taylor stochastiques we study the expansion of the solution of a stochastic differential equation as an infinite sum of iterated stochastic stratonovitch integrals this enables us to give a universal and explicit formula for any invariant diffusion on a lie group in terms of lie brackets as well as a universal and explicit formula for the brownian motion on a riemannian manifold in terms of derivatives of the curvature tensor the first of these formulae contains and extends to the non nilpotent case the results of doss 6 sussmann 17 yamato 18 fliess and normand cyrot 7 krener and lobry 19 and kunita 11 on the representation of solutions of stochastic differential equations

multiplier methods for engineering optimization multiplier methods used to solve the constrained engineering optimization problem are described these methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions the methods proposed in 1969 have been determined to be quite robust although not as efficient as other algorithms they can be more effective for some engineering applications such as optimum design and control oflarge scale dynamic systems since 1969 several modifications and extensions of the methods have been developed therefore it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications recent methods that are similar to the multiplier methods are also discussed these are continuous multiplier update exact penalty and exponential penalty methods

analysis of wiener functionals malliavin calculus and its applications to heat kernels on donne un expose facilement accessible du calcul de malliavin du calcul differentiel de dimension infinie sur l espace de wiener

stochastic delay equations with hereditary drift estimates of the density abstract we consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter e 0 we establish the asymptotic behaviour as e 0 for the logarithm of the corresponding family of densities at a fixed time t 0 the proof needs large deviation estimates and malliavin calculus

stochastic calculus with anticipating integrands we study the stochastic integral defined by skorohod in 24 of a possibly anticipating integrand as a function of its upper limit and establish an extended ito formula we also introduce an extension of stratonovich s integral and establish the associated chain rule in all the results the adaptedness of the integrand is replaced by a certain smoothness requirement

diffusions conditionnelles i hypoellipticite partielle this paper is devoted to the proof of certain results on conditional diffusions by using the malliavin calculus of variations it is shown that under minimal conditions on the vectors fields which define a two component diffusion xt zt and their lie brackets a s for any t 0 the conditional law of xt t 0 given b zs s t a c density

a stochastic sis epidemic model with vaccination abstract in this paper we investigate the basic features of an sis type infectious disease model with varying population size and vaccinations in presence of environment noise by applying the markov semigroup theory we propose a stochastic reproduction number r 0 s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence if r 0 s 1 under some mild extra conditions there exists a disease free absorbing set for the stochastic epidemic model which implies that disease dies out with probability one while if r 0 s 1 under some mild extra conditions the sde model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease the most interesting finding is that large environmental noise can suppress the outbreak of the disease

an augmented lagrangian method for distributed optimization we propose a novel distributed method for convex optimization problems with a certain separability structure the method is based on the augmented lagrangian framework we analyze its convergence and provide an application to two network models as well as to a two stage stochastic optimization problem the proposed method compares favorably to two augmented lagrangian decomposition methods known in the literature as well as to decomposition methods based on the ordinary lagrangian function

locally adaptive hazard smoothing we consider nonparametric estimation of hazard functions and their derivatives under random censorship based on kernel smoothing of the nelson 1972 estimator one critically important ingredient for smoothing methods is the choice of an appropriate bandwidth since local variance of these estimates depends on the point where the hazard function is estimated and the bandwidth determines the trade off between local variance and local bias data based local bandwidth choice is proposed a general principle for obtaining asymptotically efficient data based local bandwiths is obtained by means of weak convergence of a local bandwidth process to a gaussian limit process several specific asymptotically efficient bandwidth estimators are discussed we propose in particular an asymptotically efficient method derived from direct pilot estimators of the hazard function and of the local mean squared error this bandwidth choice method has practical advantages and is also of interest in the uncensored case as well as for density estimation

complete decomposition algorithm for nonconvex separable optimization problems and applications abstract in this paper we present a complete decomposition algorithm for nonconvex separable optimization problems applied in the optimal control problems this complete decomposition algorithm combines recursive quadratic programming with the dual method when our algorithm is applied to discretized optimal control problems a simple and parallel computation and a simple and regular data flow pattern between consecutive computational steps results this paper also suggests an approach for developing a hardware implementation of our algorithm and gives an estimation of the execution time needed to solve a practical example

on convergence of an augmented lagrangian decomposition method for sparse convex optimization a decomposition method for large scale convex optimization problems with block angular structure and many linking constraints is analysed the method is based on a separable approximation of the augmented lagrangian function weak global convergence of the method is proved and speed of convergence analysed it is shown that convergence properties of the method are heavily dependent on sparsity of the linking constraints application to large scale linear programming and stochastic programming is discussed

small time fluctuations for sub riemannian diffusion loops we study the small time fluctuations for diffusion processes which are conditioned by their initial and final positions under the assumptions that the diffusivity has a sub riemannian structure and that the drift vector field lies in the span of the sub riemannian structure in the case where the endpoints agree and the generator of the diffusion process is non elliptic at that point the deterministic malliavin covariance matrix is always degenerate we identify after a suitable rescaling another limiting malliavin covariance matrix which is non degenerate and we show that with the same scaling the diffusion malliavin covariance matrices are uniformly non degenerate we further show that the suitably rescaled fluctuations of the diffusion loop converge to a limiting diffusion loop which is equal in law to the loop we obtain by taking the limiting process of the unconditioned rescaled diffusion processes and condition it to return to its starting point the generator of the unconditioned limiting rescaled diffusion process can be described in terms of the original generator

unique stationary distribution and ergodicity of a stochastic logistic model with distributed delay abstract dynamics of a stochastic logistic model with distributed delay are considered we first transfer a scalar stochastic logistic model with strong kernel or weak kernel into an equivalent stochastic system through the linear chain technique then we obtain the sufficient and necessary conditions for extinction and persistence of the species with probability one moreover in the case of persistence we prove that there exists a unique stationary distribution by the markov semigroups theory the results show that the stronger white noise results in the extinction of the species and the weaker white noise guarantees the existence of a unique stationary distribution though for the deterministic model with strong kernel or weak kernel the average delay may induce the existence of a group of small amplitude periodic solutions

stationary distribution of a stochastic predator prey model with distributed delay and general functional response abstract in this paper we study a stochastic predator prey model with distributed delay and general functional response we transform the model with weak kernel case into an equivalent system through the linear chain technique since the diffusion matrix is degenerate the uniform ellipticity condition does not hold the markov semigroup theory is used to derive the existence of a unique stable stationary distribution we verify the densities of the distributions of the positive solutions can converge in l 1 to an invariant density

estimation de varadhan pour des diffusions a deux parametres sous des conditions de hormander generalisees la loi d une diffusion a parametre planaire possede une densite lisse en dehors des axes dans le cas elliptique nous etablissons une estimation de cette densite pur des petites valeurs du parametre celle ci constitue l analogue de l estimation de varadhan objet qui est bien connu dans le cas des diffusions ordinaires

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

malliavin calculus for the stochastic 2d navier stokes equation we consider the incompressible two dimensional navier stokes equation with periodic boundary conditions under the effect of an additive white in time stochastic forcing under mild restrictions on the geometry of the scales forced we show that any finite dimensional projection of the solution possesses a smooth strictly positive density with respect to lebesgue measure in particular our conditions are viscosity independent we are mainly interested in forcing that excites a very small number of modes all of the results rely on proving the nondegeneracy of the infinite dimensional malliavin matrix c 2006 wiley periodicals inc

stationary distribution of a stochastic sis epidemic model with vaccination abstract in this paper we consider a stochastic sis epidemic model with vaccination we prove that the densities of the distributions of the solution can converge in l 1 to an invariant density under appropriate conditions also we find the support of the invariant density

a new technique for nonconvex primal dual decomposition of a large scale separable optimization problem the primal dual approach is quite effective in decomposing a convex separable optimization problem into several subproblems of smaller sizes in this paper we present a new technique which extends the primal dual approach to nonconvex problems since a straightforward application of the multiplier method destroys separability a new lagrangian function is proposed which preserves separability based on this new function we develop a new iterative method for finding an optimal solution to the problem and show that the method is locally convergent to an optimal solution furthermore the effect of certain parameters on the ratio of convergence is investigated and simple examples are given to illustrate the proposed approach

transformations in density estimation abstract for the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations in this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data the density estimate of the original data is the back transform by change of variables of the global window width estimate of the transformed data s density we explore choosing the transformation from suitable parametric families data based selection rules for the choice of transformations and the window width are discussed application to real and simulated data demonstrates the usefulness of our proposals

asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples abstract this paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship first an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given second it is shown that if the bandwidth is chosen by the data based method of least squares cross validation then it is asymptotically optimal in a compelling sense a by product of the first part is an interesting comparison of the two most popular kernel estimators keywords nonparametric density estimation smoothing parameter

positivity theorem in semi group theory we translate in semi group theory the proof of the theorem of ben arous and ourself got by the malliavin calculus giving a sufficient condition involved with the bismutian distance such that an heat kernel is strictly positive

long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator abstract second order subelliptic operators have been the subject of a considerable amount of research in recent years starting with the paper rothschild and stein in which the sharp form of hormander s famous subellipticity theorem is proved and continuing through the work of fefferman and phong and sanchez calle it has become increasingly clear that precise regularity estimates for these operators depend intimately on the geometry associated with the operator under consideration the main purpose of this article is to obtain bounds from above and below on p t x y t epsilon 1 infinity in terms of standard heat kernels

marginal density expansions for diffusions and stochastic volatility ii applications in 17 we discussed density expansions for multidimensional diffusions x 1 x d at fixed time t and projected to their first l coordinates in the small noise regime global conditions were found which replace the well known not in cutlocus condition known from heat kernel asymptotics in the present paper we discuss financial applications these include tail and implied volatility asymptotics in some correlated stochastic volatility models in particular we solve a problem left open by a gulisashvili and e m stein 2009

logarithmic estimates for the density of hypoelliptic two parameter diffusions we consider a hypoelliptic two parameter diffusion we first prove a sharp upper bound in small time s t 0 1 2 for the lp moments of the inverse of the malliavin matrix of the diffusion process second we establish the behaviour of2e2logps t x y as e 0 where x is the initial condition of the diffusion e st and ps t x y is the density of the hypoelliptic two parameter diffusion

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

in sample forecasting with local linear survival densities in this paper in sample forecasting is defined as forecasting a structured density to sets where it is unobserved the structured density consists of one dimensional in sample components that identify the density on such sets we focus on the multiplicative density structure which has recently been seen as the underlying structure of non life insurance forecasts in non life insurance the in sample area is defined as one triangle and the forecasting area as the triangle that 20 added to the first triangle produces a square recent approaches estimate two one dimensional components by projecting an unstructured two dimensional density estimator onto the space of multiplicatively separable functions we show that time reversal reduces the problem to two one dimensional problems where the one dimensional data are left truncated and a one dimensional survival density estimator is needed this paper then uses the local linear density smoother with 25 weighted cross validated and do validated bandwidth selectors full asymptotic theory is provided with and without time reversal finite sample studies and an application to non life insurance are included

the coexistence of a stochastic lotka volterra model with two predators competing for one prey in this paper we consider a stochastic lotka volterra model with two predators competing for one prey we give the sufficient conditions which guarantee that the principle of coexistence holds for this perturbed model via markov semigroup theory furthermore we prove that the densities of the solution can converge in l1 to an invariant density under appropriate conditions finally we make simulations to illustrate our analytical results

nonparametric kernel estimation in counting processes with explanatory variables summary cox s proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonnegative function of explanatory variables an estimate of the baseline hazard rate hence also of overall hazard rate is proposed based on a smoothing procedure using a kernel function it is shown that the proposed estimator is uniformly consistent and converges weakly to a gaussian process bandwidth selection issues are also discussed

quotient of a loop group and witten genus we define a dirac ramond operator over the quotient lg h of a loop group by a subgroup h of the compact lie group g we state the conjecture that its equivariant index with respect of the natural circle action over the quotient of the loop group is equal to the witten genus of the homogeneous manifold g h we motivate the conjecture by a short time argument which allows to come back to a dirac ramond operator at the manner of taubes on a limit model where all the computations can be done by hand

marginal density expansions for diffusions and stochastic volatility i theoretical foundations density expansions for hypoelliptic diffusions x1 xd are revisited we are particularly interested in density expansions of the projection at time t 0 with l d global conditions are found that replace the well known not in cut locus condition known from heat kernel asymptotics our small noise expansion allows for a second order exponential factor as an application new light is shed on the takanobu watanabe expansion of brownian motion and levy s stochastic area further applications include tail and implied volatility asymptotics in some stochastic volatility models discussed in the companion paper 12 2013 wiley periodicals inc

density estimates for a random noise propagating through a chain of differential equations we here provide two sided bounds for the density of the solution of a system of n differential equations of dimension d the first one being forced by a non degenerate random noise and the n 1 other ones being degenerate the system formed by the n equations satisfies a suitable hormander condition the second equation feels the noise plugged into the first equation the third equation feels the noise transmitted from the first to the second equation and so on so that the noise propagates one way through the system when the coefficients of the system are lipschitz continuous we show that the density of the solution satisfies gaussian bounds with non diffusive time scales the proof relies on the interpretation of the density of the solution as the value function of some optimal stochastic control problem

decroissance non exponentielle du noyau de la chaleur in this paper we give estimates on the heat kernel on the diagonal in terms of exp logt 1 when1 vanishes moreover we compute by means of the stochastic calculus of variations the decay of the flatness of some heat kernels on the other hand we show that the computations in both cases are very similar

the rate function of hypoelliptic diffusions let be a hypoelliptic diffusion operator on a compact manifold m given an a priori smooth reference measure on m we can then rewrite l as the sum of a symmetric part l0 and a first order drift part y the paper investigates the effect of the drift y on the donsker varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion when y is in the linear span of the first and second order lie brackets of the xi s we derive an affine bound relating the rate functions associated with l and l0 as soon as one point exists where y is not in the linear span of the first and second order lie brackets of the xi s we show that such an affine bound is impossible 1994 john wiley sons inc

a stochastic sirs epidemic model with infectious force under intervention strategies abstract in this paper we extend a classical sirs epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation sde one through introducing random fluctuations the value of our study lies in two aspects mathematically by using the markov semigroups theory we prove that the reproduction number r 0 s can be used to govern the stochastic dynamics of sde model if r 0 s 1 under mild extra conditions the sde system has a disease free absorbing set which means the extinction of disease with probability one if r 0 s 1 under mild extra conditions it has an endemic stationary distribution which leads to the stochastical persistence of the disease epidemiologically we find that random fluctuations can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

curvature terms in small time heat kernel expansion for a model class of hypoelliptic hormander operators we consider the heat equation associated with a class of second order hypoelliptic h o rmander operators with constant second order term and linear drift we describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature like invariants of the optimal control problem associated with the diffusion operator

stationary distribution of a stochastic siqr epidemic model with saturated incidence and degenerate diffusion abstract the objective of this paper is to study stationary distribution of a stochastic siqr epidemic model with saturated incidence and degenerate diffusion since the diffusion matrix is degenerate the uniform ellipticity condition is not satisfied the markov semigroup theory will be used to obtain the existence of a unique stable stationary distribution a threshold dynamic determined by the basic reproduction number r 0 s is established the disease can be eradicated almost surely if r 0 s 1 whereas if r 0 s 1 it has an endemic stationary distribution which leads to the stochastic persistence of the disease

asymptotic ergodicity of the process of conditional law in some problem of non linear filtering abstract we consider a sample of a trajectory of an ergodic process m x through a stationary noisy observation process we study the asymptotic ergodicity of the phase process