equations differentielles sur l espace de wiener et formules de cameron martin non lineaires proprietes algebriques des approximations sur r n une formule de perturbation des flots et convergence des approximations formule de changement de variable sur x et equation differentielle

are fmri event related response constant in time a model selection answer an accurate estimation of the hemodynamic response function hrf in functional magnetic resonance imaging fmri is crucial for a precise spatial and temporal estimate of the underlying neuronal processes recent works have proposed non parametric estimation of the hrf under the hypotheses of linearity and stationarity in time biological literature suggests however that response magnitude may vary with attention or ongoing activity we therefore test a more flexible model that allows for the variation of the magnitude of the hrf with time in a maximum likelihood framework under this model the magnitude of the hrf evoked by a single event may vary across occurrences of the same type of event this model is tested against a simpler model with a fixed magnitude using information theory we develop a standard em algorithm to identify the event magnitudes and the hrf we test this hypothesis on a series of 32 regions 4 rois on eight subjects of interest and find that the more flexible model is better than the usual model in most cases the important implications for the analysis of fmri time series for event related neuroimaging experiments are discussed

girsanov identities for poisson measures under quasi nilpotent transformations we prove a girsanov identity on the poisson space for anticipating transformations that satisfy a strong quasi nilpotence condition applications are given to the girsanov theorem and to the invariance of poisson measures under random transformations the proofs use combinatorial identities for the central moments of poisson stochastic integrals

the method of gauss newton to compute power series solutions of polynomial homotopies abstract we consider the extension of the method of gauss newton from complex floating point arithmetic to the field of truncated power series with complex floating point coefficients with linearization we formulate a linear system where the coefficient matrix is a series with matrix coefficients and provide a characterization for when the matrix series is regular based on the algebraic variety of an augmented system the structure of the linear system leads to a block triangular system in the regular case solving the linear system is equivalent to solving a hermite interpolation problem we show that this solution has cost cubic in the problem size in general at singular points we rely on methods of tropical algebraic geometry to compute puiseux series with a few illustrative examples we demonstrate the application to polynomial homotopy continuation

a polynomial time complexity bound for the computation of the singular part of a puiseux expansion of an algebraic function in this paper we present a refined version of the newton polygon process to compute the puiseux expansions of an algebraic function defined over the rational function field we determine an upper bound for the bit complexity of computing the singular part of a puiseux expansion by this algorithm and use a recent quantitative version of eisenstein s theorem on power series expansions of algebraic functions to show that this computational complexity is polynomial in the degrees and the logarithm of the height of the polynomial defining the algebraic function

transformation of wiener measure under anticipative flows lett f be a transformation from the wiener space to itself with the range off assumed to be in the cameron martin space the absolute continuity and the density function associated witht is considered t is assumed to be embedded in or defined through a parameterizationt t f t andf t is assumed to be differentiable int the paper deals first with the case where the range of thet derivative off t is also in the cameron martin space and new representations for the radon nikodym derivative and the carleman fredholm determinant are derived the case where thet derivative off t is not in the cameron martin space is considered next and results on the absolute continuity and the density function under conditions which are considerably weaker than previously known conditions are presented

a state space model of the hemodynamic approach nonlinear filtering of bold signals in this paper a new procedure is presented which allows the estimation of the states and parameters of the hemodynamic approach from blood oxygenation level dependent bold responses the proposed method constitutes an alternative to the recently proposed friston neuroimage 16 2002 513 method and has some advantages over it the procedure is based on recent groundbreaking time series analysis techniques that have been in this case adopted to characterize hemodynamic responses in functional magnetic resonance imaging fmri this work represents a fundamental improvement over existing approaches to system identification using nonlinear hemodynamic models and is important for three reasons first our model includes physiological noise previous models have been based upon ordinary differential equations that only allow for noise or error to enter at the level of observation secondly by using the innovation method and the local linearization filter not only the parameters but also the underlying states of the system generating responses can be estimated these states can include things like a flow inducing signal triggered by neuronal activation de oxyhemoglobine cerebral blood flow and volume finally radial basis functions have been introduced as a parametric model to represent arbitrary temporal input sequences in the hemodynamic approach which could be essential to understanding those brain areas indirectly related to the stimulus hence thirdly by inferring about the radial basis parameters we are able to perform a blind deconvolution which permits both the reconstruction of the dynamics of the most likely hemodynamic states and also to implicitly reconstruct the underlying synaptic dynamics induced experimentally which caused these states variations from this study we conclude that in spite of the utility of the standard discrete convolution approach used in statistical parametric maps spm nonlinear bold phenomena and unspecific input temporal sequences must be included in the fmri analysis

homotopies exploiting newton polytopes for solving sparse polynomial systems this paper is concerned with the problem of finding all isolated solutions of a polynomial system the bkk bound defined as the mixed volume of the newton polytopes of the polynomials in the system is a sharp upper bound for the number of isolated solutions in mathbb c 0 n mathbb c 0 mathbb c backslash 0 of a polynomial system with a sparse monomial structure first an algorithm is described for computing the bkk bound following the lines of bernshtei n s proof the algorithmic construction of the cheater s homotopy or the coefficient homotopy is obtained the mixed homotopy methods can be combined with the random product start systems based on a generalized bezout number applications illustrate the effectiveness of the new approach

characterizing stimulus response functions using nonlinear regressors in parametric fmri experiments parametric study designs proved very useful in characterizing the relationship between experimental parameters e g word presentation rate and regional cerebral blood flow in positron emission tomography studies in a previous paper we presented a method that fits nonlinear functions of stimulus or task parameters to hemodynamic responses using second order polynomial expansions here we expand this approach to model nonlinear relationships between bold responses and experimental parameters using fmri we present a framework that allows this technique to be implemented in the context of the general linear model employed by statistical parametric mapping spm statistical inferences in this instance are based on f statistics and in this respect we emphasize the use of corrected p values for f fields i e spm5f6 the approach is illustrated with a fmri study that looked at the effect of increasing auditory word presentation rate our parametric design allowed us to characterize different forms of rate dependent responses in three critical regions i bilateral frontal regions showed a categorical response to the presence of words irrespective of rate suggesting a role for this region in establishing cognitive e g attentional set ii in bilateral occipitotemporal regions activations increased linearly with increasing word rate and iii posterior auditory association cortex exhibited a nonlinear inverted u relationship to word rate r 1998 academic press

polynomial equation solving by lifting procedures for ramified fibers let be given a parametric polynomial equation system which represents a generically unramified family of zero dimensional algebraic varieties we exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of the infinitesimal structure of a particular ramified parameter instance of our family this generalizes in the case of space curves previous methods of heintz et al and schost which require the given parameter instance to be unramified we illustrate our method solving particular polynomial equation systems by deformation techniques

anticipative girsanov transformations the transformations of measures induced by left w int limits 0 bullet k s ds right with ks possibly anticipating the wiener process ws is discussed and a girsanovtype theorem under rather weak assumptions on ks is derived

girsanov theorem for anticipative shifts on poisson space we study the absolute continuity of the image measure of the canonical poisson probability measure under nonlinear shifts the radon nykodim density function is expressed using a carleman fredholm determinant and a divergence operator results are obtained for non necessarily invertible transformations under almost sure differentiability hypothesis

a polyhedral method for solving sparse polynomial systems a continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations we introduce mixed subdivisions of newton polytopes and we apply them to give a new proof and algorithm for bernstein s theorem on the expected number of roots this results in a numerical homotopy with the optimal number of paths to be followed in this homotopy there is one starting system for each cell of the mixed subdivision and the roots of these starting systems are obtained by an easy combinatorial construction

formes de dirichlet generales et densite des variables aleatoires reelles sur l espace de wiener abstract it is shown that the main properties of dirichlet spaces can be proved without the classical local compacity hypothesis to this purely measurable framework we extend the functional calculus and the energy image density property these results are then applied to the ornstein uhlenbeck semi group on wiener space where it is obtained that the real random variables which are solutions of lipschitzian stochastic differential equations always have probability densities after perhaps an initial deterministic phase

deformation techniques to solve generalised pham systems in heintz et al electron j sadio 1 1 1998 37 castro et al found comput math 2003 to appear and pardo proceedings eaca 2000 2000 pp 25 51 the authors have shown that universal solving procedures require exponential running time roughly speaking a universal solving procedure takes as input a system of multivariate polynomial equations and outputs complete symbolic information on the solution variety here we introduce a nonuniversal solving procedure adapted to generalised pham systems the aim is to compute partial information of the variety defined by the input system the algorithm is based on an homotopic deformation and on a non archimedean lifting procedure from a non singular zero of the homotopy curve the complexity of the procedure is also stated and it depends on some intrinsic quantity called the deformation degree of the given input system

linear skorohod stochastic differential equations let andb be bounded processes on the wiener space p c 0 1 which are possibly anticipating the brownian motionw t t and let be a bounded random variable we deduce the existence and uniqueness of a solutionx for the linear equation with skorohod integral x t eta int limits 0 t sigma s x s dw s int limits 0 t b s x s ds t in 0 1 1 under rather weak assumptions on and no additional requirement onb and the description of the solutionx requires to study the family t t t 0 1 of transformationt t of into itself associated to 1 by the equation t t omega int limits 0 t wedge sigma s t s omega ds omega in omega t in 0 1

definability and fast quantifier elimination in algebraically closed fields abstract the bezout inequality an affine version not including multiplicities of the classical bezout theorem is derived for applications in algebraic complexity theory upper bounds for the cardinality and number of sets definable by first order formulas over algebraically closed fields are given this is used for fast quantifier elimination in algebraically closed fields

transformation of the wiener measure under non invertible shifts in this paper we consider the transformation of measure induced by a not necessarily invertible perturbation of the identity the radon nikodym density for the image of the wiener measure and the associated girsanov type density are derived an application of these results yields an extension of the degree theorem

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography