a remark on regularity criterion for the 3d hall mhd equations based on the vorticity in this paper we investigate the regularity criterion for the local in time classical solution to the three dimensional 3d incompressible hall magnetohydrodynamic equations hall mhd it is proved that the control of the vorticity alone can ensure the smoothness of the solution

random rotations of the wiener path let w h be an abstract wiener space and letr w be a strongly measurable random variable with values in the set of isometries onh suppose that rh is smooth in the sobolev sense and that it is a quasi nilpotent operator onh for everyh h it is shown that r w h is again a gaussian 0 h 2 random variable consequently if e i i w is a complete orthonormal basis ofh then tilde w sum nolimits i delta r w e i e i defines a measure preserving transformation a rotation onw it is also shown that if for some strongly measurable operator valued onh random variabler r w k h is 0 h 2 gaussian for allk h h thenr is an isometry and rh is quasi nilpotent for allh h the relation between the stochastic calculi for these wiener pathsw and tilde w as well as the conditions of the inverbibility of the map w to tilde w are discussed and the problem of the absolute continuity of the image of the wiener measure under euclidean motion on the wiener space i e w to tilde w composed with a shift is studied

how general is the vale maurelli simulation approach the vale maurelli vm approach to generating non normal multivariate data involves the use of fleishman polynomials applied to an underlying gaussian random vector this method has been extensively used in monte carlo studies during the last three decades to investigate the finite sample performance of estimators under non gaussian conditions the validity of conclusions drawn from these studies clearly depends on the range of distributions obtainable with the vm method we deduce the distribution and the copula for a vector generated by a generalized vm transformation and show that it is fundamentally linked to the underlying gaussian distribution and copula in the process we derive the distribution of the fleishman polynomial in full generality while data generated with the vm approach appears to be highly non normal its truly multivariate properties are close to the gaussian case a monte carlo study illustrates that generating data with a different copula than that implied by the vm approach severely weakens the performance of normal theory based ml estimates

simulating multivariate nonnormal distributions a method for generating multivariate nonnormal distributions with specified intercorrelations and marginal means variances skews and kurtoses is proposed as an example the method is applied to the generation of simulated scores on three psychological tests administered to a single group of individuals

a poincare inequality on loop spaces we show that the laplacian on the loop space over a class of riemannian manifolds has a spectral gap the laplacian is defined using the levi civita connection the brownian bridge measure and the standard bismut tangent spaces

generating correlated non normally distributed data using a non linear structural model an approach to generate non normality in multivariate data based on a structural model with normally distributed latent variables is presented the key idea is to create non normality in the manifest variables by applying non linear linking functions to the latent part the error part or both the algorithm corrects the covariance matrix for the applied function by approximating the deviance using an approximated normal variable we show that the root mean square error rmse for the covariance matrix converges to zero as sample size increases and closely approximates the rmse as obtained when generating normally distributed variables our algorithm creates non normality affecting every moment is computationally undemanding easy to apply and particularly useful for simulation studies in structural equation modeling

global wellposedness for hall mhd equations abstract this paper concerns the wellposedness problem of hall mhd system the mild solution of hall mhd equations exists globally in the nonhomogeneous lei lin space setting provided that the initial data satisfies u 0 x 1 x 0 b 0 x 1 x 0 min 2 4 where is the viscosity of the fluid and is the magnetic diffusion coefficient our global existence result covers rougher initial data and improves the previous results

the vanishing of l2 harmonic one forms on based path spaces abstract we prove the triviality of the first l 2 cohomology class of based path spaces of riemannian manifolds furnished with brownian motion measure and the consequent vanishing of l 2 harmonic one forms we give explicit formulae for closed and co closed one forms expressed as differentials of functions and co differentials of l 2 two forms respectively these are considered as extended clark ocone formulae a feature of the proof is the use of the temporal structure of path spaces to relate a rough exterior derivative operator on one forms to the exterior differentiation operator used to construct the de rham complex and the self adjoint laplacian on l 2 one forms this laplacian is shown to have a spectral gap

a class of invariant procedures for assessing multivariate normality summary distribution theory pertaining to a class of invariant procedures for assessing multivariate normality is described a cramer von mises type statistic belonging to this class is investigated in greater detail its asymptotic distribution is tabulated and compared with a monte carlo simulation of its finite sample distribution and a set of quadrivariate data is examined with it

de rham hodge kodaira operator on loop groups we consider a based loop group le g over a compact lie groupg endowed with its pinned wiener measure the law of the brownian bridge ong and we shall calculate the ricci curvature for differentialn forms over le g a type of bochner weitzenbock formula for general differentialn forms or shigekawa identity will be established

tangent processes on wiener space abstract this paper deals with the study of the malliavin calculus of euclidean motions on wiener space i e transformations induced by general measure preserving transformations called rotations and h valued shifts and the associated flows on abstract wiener spaces

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

anl2estimate for riemannian anticipative stochastic integrals abstract we define a metric and a markovian connection on the path space of a riemannian manifold which are different from those introduced in cm and prove a corresponding weitzenbock formula an l 2 inequality for the divergence is obtained as a consequence

a new test for multivariate normality and homoscedasticity given data x ij j 1 to n i i 1 to g one may wish to test whether the x ij are normal with common covariance matrix letting x i denote the mean of the ith group and s the pooled covariance matrix the quantities v ij x ij x i s 1 x ij x i are used in the test the exact null distribution of v ij is noted and the anderson darling statistic is proposed for testing whether the data fit this null distribution the new test has acceptable power is flexible and is easily implemented

adaptive smoothing and density based tests of multivariate normality abstract methods of adaptive smoothing of density estimates where the amount of smoothing applied varies according to local features of the underlying density are investigated the difficulties of applying taylor series arguments in this context are explored simple properties of the estimates are investigated by numerical integration and compared with the fixed kernel approach optimal smoothing strategies based on the multivariate normal distribution are derived as an application of these techniques two tests of multivariate normality one based on integrated squared error and one on entropy are developed and some power calculations are carried out

a regularity criterion for a generalized hall mhd system abstract this paper proves a regularity criterion for a 3d generalized hall mhd system in terms of velocity gradient in negative besov spaces

on the blow up criterion and small data global existence for the hall magnetohydrodynamics abstract in this paper we establish an optimal blow up criterion for classical solutions to the incompressible resistive hall magnetohydrodynamic equations we also prove two global in time existence results of the classical solutions for small initial data the smallness conditions of which are given by the suitable sobolev and the besov norms respectively although the sobolev space version is already an improvement of the corresponding result in 4 the optimality in terms of the scaling property is achieved via the besov space estimate the special property of the energy estimate in terms of b 2 1 s norm is essential for this result contrary to the usual mhd the global well posedness in the 2 1 2 dimensional hall mhd is wide open

logarithmic sobolev inequalities on loop groups let g be a compact lie group denote by m the brownian bridge measure on the loop group y g c 0 1 g g 0 g 1 e the finite energy subgroup of y determines in a natural way a gradient operation for functions on y the following logarithmic sobolev inequality is proven f2 log f dm gradf y 2 v y f y 2 dm f 2log f wherein f denotes the l2 m norm and v is a potential which is quadratic in the associated lie algebra valued brownian motion the inequality is derived by a method of inheritance from the known inequality for the g valued brownian motion

analysis on wiener spaces ii differential forms abstract the author gives the notions of p forms and p forms and shows some properties of them in particular a vanishing theorem of de rham cohomology of poincare type also he shows the hypoellipticity of certain elliptic operators on wiener space and a theorem of poinare inequality type

a cameron martin type quasi invariance theorem for pinned brownian motion on a compact riemannian manifold the results in driver 13 for quasi invariance of wiener measure on the path space of a compact riemannian manifold m are extended to the case of pinned wiener measure to be more explicit let h 0 1 tom be a c1 function where m is a compact riemannian manifold o e m is a base point and tom is the tangent space to m at o e m let w m be the space of continuous paths from 0 1 into m v be wiener measure on w m concentrated on paths starting at o e m and hs w denote the stochastic parallel translation operator along a path to e w m up to time s note hs w is only well defined up to v equivalence for c e w m let xh w denote the vector field along a given by xsh c hs cw h s for each s e 0 1 one should interpret xh as a vector field on w m the vector field xh induces a flow sh t w m w m which leaves wiener measure v quasi invariant see driver 13 it is shown in this paper that the same result is valid if h l 0 and the wiener measure v is replaced by a pinned wiener measure ive the measure ve is proportional to the measure v conditioned on the set of paths which start at 0 e m and end at a fixed end point e e m also as in 13 one gets an integration by parts formula for the vector fields xh defined above

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

covariance model simulation using regular vines we propose a new and flexible simulation method for non normal data with user specified marginal distributions covariance matrix and certain bivariate dependencies the vita vine to anything method is based on regular vines and generalizes the norta normal to anything method fundamental theoretical properties of the vita method are deduced two illustrations demonstrate the flexibility and usefulness of vita in the context of structural equation models r code for the implementation is provided

heat equation derivative formulas for vector bundles we use martingale methods to give bismut type derivative formulas for differentials and co differentials of heat semigroups on forms and more generally for sections of vector bundles the formulas are mainly in terms of weitzenbock curvature terms in most cases derivatives of the curvature are not involved in particular our results improve b k driver s formula in 1997 j math pures appl 9 76 703 737 for logarithmic derivatives of the heat kernel measure on a riemannian manifold our formulas also include the formulas of k d elworthy and x m li 1998 c r acad sci paris ser i math 327 87 92

weak levi civita connection for the damped metric on the riemannian path space and vanishing of ricci tensor in adapted differential geometry abstract we shall establish in the context of adapted differential geometry on the path space p m o m a weitzenbock formula which generalizes that in a b cruzeiro and p malliavin j funct anal 177 2000 219 253 without hypothesis on the ricci tensor the renormalized ricci tensor will be vanished the connection introduced in a b cruzeiro and s fang 1997 j funct anal 143 400 414 will play a central role

markovian connection curvature and weitzenbock formula on riemannian path spaces abstract we shall consider on a riemannian path space p m o m the cruzeiro malliavin s markovian connection the laplace operator will be defined as the divergence of the gradient we shall compute explicitly the associated curvature tensor a weitzenbock formula will be established to this end we shall introduce an inner product between the tangent processes and simple vector fields

logarithmic sobolev inequalities and exponential integrability we prove the exponential integrability of lipschitz functions in abstract wiener spaces by using logarithmic sobolev inequalities we introduce two notions of lipschitz continuity and apply the method of davis and simon j funct anal 59 1984 335 395 to prove our main theorem moreover we give several conditions under which the function is exponentially integrable

finite dimensional approximation of riemannian path space geometry abstract in this paper we construct a finite dimensional approximation for the geometry on the path space over a compact riemannian manifold this approximation allows to construct the horizontal lift of the ornstein uhlenbeck process on the path space through the markovian connection we also prove a representation formula for the heat semigroup on adapted vector fields as well as a commutation formula for its derivative

a remark on the blow up criterion for the 3d hall mhd system in besov spaces abstract in this paper we consider the three dimensional hall magnetohydrodynamic system and show that if the velocity and the magnetic fields belong to some critical besov spaces on 0 t then the solution can be extended smoothly beyond t this improves previous results

the divergence on submanifolds of the wiener space abstract using malliavin s calculus the divergence the covariant derivative and the riemann and ricci curvatures of a submanifold of the wiener space are defined it is shown that the ricci and riemann curvatures appear in the commutator of the divergence operator and covariant derivative operator capacities are used to restrict the commutator formula to a submanifold and to deduce that the curvature belongs to all l p da spaces where a is the area measure associated to the submanifold a version of weitzenbock s formula a bochner type formula and a criterion for the existence of the divergence are proved a generalization to higher dimensional tensor fields is stated and a connection with stochastic integration on the submanifold of the wiener space is worked out

the log sobolev inequality on loop space over a compact riemannian manifold abstract we obtain a log sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact riemannian manifold the potential term relies only on the curvature of the manifold and the hessian of the heat kernel and is l p integrable for all p 1 the log sobolev inequality is derived by a martingale representation theorem for the differentiable functions on loop space which is a variation of the clark ocone haussmann formula

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

functional inequality on path space over a non compact riemannian manifold abstract we prove the existence of the o u dirichlet form and the damped o u dirichlet form on path space over a general non compact riemannian manifold which is complete and stochastically complete we show a weighted log sobolev inequality for the o u dirichlet form and the standard log sobolev inequality for the damped o u dirichlet form in particular the poincare inequality and the super poincare inequality can be established for the o u dirichlet form on path space over a class of riemannian manifolds with unbounded ricci curvatures moreover we construct a large class of quasi regular local dirichlet forms with unbounded random diffusion coefficients on path space over a general non compact manifold

a problem with discretizing vale maurelli in simulation studies previous influential simulation studies investigate the effect of underlying non normality in ordinal data using the vale maurelli vm simulation method we show that discretized data stemming from the vm method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector this normal vector has however a different covariance matrix than the target it follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure this observation affects the interpretation of previous simulation studies

simulation of massive public health data by power polynomials situations in which multiple outcomes and predictors of different distributional types are collected are becoming increasingly common in public health practice and joint modeling of mixed types has been gaining popularity in recent years evaluation of various statistical techniques that have been developed for mixed data in simulated environments necessarily requires joint generation of multiple variables most massive public health data sets include different types of variables for instance in clustered or longitudinal designs often multiple variables are measured or observed for each individual or at each occasion this work is motivated by a need to jointly generate binary and possibly non normal continuous variables we illustrate the use of power polynomials to simulate multivariate mixed data on the basis of a real adolescent smoking study we believe that our proposed technique for simulating such intensive data has potential to be a handy methodological addition to public health researchers toolkit

divergence theorems in path space abstract we obtain divergence theorems on the solution space of an elliptic stochastic differential equation defined on a smooth compact finite dimensional manifold m the resulting divergences are expressed in terms of the ricci curvature of m with respect to a natural metric on m induced by the stochastic differential equation the proofs of the main theorems are based on the lifting method of malliavin together with a fundamental idea of driver

quasi invariance of the wiener measure on the path space over a complete riemannian manifold we prove a generalization of the cameron martin theorem for a geometrically and stochastically complete riemannian manifold namely the wiener measure on the path space over such a manifold is quasiinvariant under the flow generated by a cameron martin vector field

generalized radius processes for elliptically contoured distributions the use of mahalanobis distances has a long history in statistics given a sample of size n and general location and scatter estimators mn and n we can define generalized radii as if we wish to trim observations based on the estimators mn and n then it is natural to first remove the most remote ones i e those with the largest s with this in mind we define a process that maps the trimming proportion in 0 1 to the generalized radius of the observation that has just been removed by this level of trimming we analyze the asymptotic behavior of this process for elliptically contoured distributions we show that the limit law depends only on the elliptical family considered and how n serves to estimate the underlying scale factor through its determinant we carry out monte carlo simulations for finite sample sizes and outline an application for assessing fit to a fixed elliptical family and also for the case where a proportion of outlying observations is discarded

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

gaussian mixture modeling by exploiting the mahalanobis distance in this paper the expectation maximization em algorithm for gaussian mixture modeling is improved via three statistical tests the first test is a multivariate normality criterion based on the mahalanobis distance of a sample measurement vector from a certain gaussian component center the first test is used in order to derive a decision whether to split a component into another two or not the second test is a central tendency criterion based on the observation that multivariate kurtosis becomes large if the component to be split is a mixture of two or more underlying gaussian sources with common centers if the common center hypothesis is true the component is split into two new components and their centers are initialized by the center of the old component candidate for splitting otherwise the splitting is accomplished by a discriminant derived by the third test this test is based on marginal cumulative distribution functions experimental results are presented against seven other em variants both on artificially generated data sets and real ones the experimental results demonstrate that the proposed em variant has an increased capability to find the underlying model while maintaining a low execution time

an l 2 theory for differential forms on path spaces i an l 2 theory of differential forms is proposed for the banach manifold of continuous paths on a riemannian manifold m furnished with its brownian motion measure differentiation must be restricted to certain hilbert space directions the h tangent vectors to obtain a closed exterior differential operator the relevant spaces of differential forms the h forms are perturbed by the curvature of m a hodge decomposition is given for l 2 h one forms and the structure of h two forms is described the dual operator d is analysed in terms of a natural connection on the h tangent spaces malliavin calculus is a basic tool c 2007 elsevier inc all rights reserved

a class of processes on the path space over a compact riemannian manifold with unbounded diffusion a class of diffusion processes on the path space over a compact riemannian manifold is constructed the diffusion of such a process is governed by an unbounded operator a representation of the associated generator is derived and the existence of a certain local second moment is shown

modified models and simulations for estimating dynamic functional connectivity in resting state functional magnetic resonance imaging as understanding the nature of brain networks through dynamic functional connectivity dfc estimation is of paramount significant the introduction and revision of blood oxygen level dependent bold signal simulation methods in brain regions and dfc estimation methods have gained significant ground in recent years based on the observation of bold signals with multivariate nonnormal distribution in functional magnetic resonance imaging fmri images we first propose a copula based method for the production of these signals in which nonnormal data are generated with a selected time varying covariance matrix therefore we can compare the performance of models in the cases where brain signals have a multivariate nonnormal distribution then two kendallized exponentially weighted moving average kewma and kendallized dynamic conditional correlation kdcc multivariate volatility models are introduced which are based on two well known and commonly used exponentially weighted moving average emwa and dynamic conditional correlation dcc models the results show that kdcc model can estimate conditional correlation significantly far better than the former ones ie dcc standardized dynamic conditional correlation ewma and standardized exponentially weighted moving average on both types of data ie multivariate normal and nonnormal in the next step the bivariate normal distribution in iranian resting state fmri data is confirmed by using statistical tests and it is shown that the dynamic nature of fc is not optimally detected using prevalent methods two alternative portmanteau and rank based tests are proposed for the examination of conditional heteroscedasticity in data finally dfc in these data is estimated by employing the kdcc model

logarithmic derivatives of heat kernels and logarithmic sobolev inequalities with unbounded diffusion coefficients on loop spaces abstract in this paper we will give a sufficient condition on the logarithmic derivative of the heat kernel under which a logarithmic sobolev inequality lsi in abbreviation on a loop space holds as an application we prove an lsi on a pinned path space over the hyperbolic space h n with constant sectional curvature a a 0 the diffusion coefficient of the dirichlet form is an unbounded but exponentially integrable function applying to the case when a 0 we can prove an lsi with a logarithmic sobolev constant 18 in the case of standard pinned brownian motion using the lsi on the pinned path space on h n we will prove an lsi on each homotopy class of the loop space over a constant negative curvature compact riemannian manifold

goodman and kruskal s gamma coefficient for ordinalized bivariate normal distributions we consider a bivariate normal distribution with linear correlation formula see text whose random components are discretized according to two assigned sets of thresholds on the resulting bivariate ordinal random variable one can compute goodman and kruskal s gamma coefficient formula see text which is a common measure of ordinal association given the known analytical monotonic relationship between pearson s formula see text and kendall s rank correlation formula see text for the bivariate normal distribution and since in the continuous case kendall s formula see text coincides with goodman and kruskal s formula see text the change of this association measure before and after discretization is worth studying we consider several experimental settings obtained by varying the two sets of thresholds or equivalently the marginal distributions of the final ordinal variables this study confirming previous findings shows how the gamma coefficient is always larger in absolute value than kendall s rank correlation this discrepancy lessens when the number of categories increases or given the same number of categories when using equally probable categories based on these results a proposal is suggested to build a bivariate ordinal variable with assigned margins and goodman and kruskal s formula see text by ordinalizing a bivariate normal distribution illustrative examples employing artificial and real data are provided

logarithmic sobolev inequalities for pinned loop groups abstract letgbe a connected compact type lie group equipped with anadg invariant inner product on the lie algebra g ofg given this data there is a well known left invariant h1 riemannian structure on l l g the infinite dimensional group of continuous based loops ing using this riemannian structure we define and construct a heat kernel t g0 associated to the laplace beltrami operator on l g heret 0 g0 l g and t g0 is a certain probability measure on l g for fixedg0 l g andt 0 we use the measure t g0 and the riemannian structure on l g to construct a classical pre dirichlet form the main theorem of this paper asserts that this pre dirichlet form admits a logarithmic sobolev inequality

stochastic analysis on the path space of a riemannian manifold i markovian stochastic calculus abstract on the brownian flow of a compact riemannian manifold an intrinsic stochastic calculus is defined this calculus is markovian the stochastic calculus of variation on the bundle of orthonormal frames appears only as an intermediate tool the bismut connection plays a paramount role in the final construction

on assessing multivariate normality summary we discuss procedures for assessing multivariate normality based on properties of radii and angles of the multivariate normal distribution and suggest that different procedures may be efficiently combined in order to achieve omnibus tests the assumption of population multivariate normality underlies many multivariate data analytic procedures unfortunately however there are relatively few formal methods available for assess ing the validity of this underlying assumption gnanadesikan 1977 section 5 4 2 and cox and small 1978 have extensively reviewed various formal and informal procedures proposed for testing the multinormality hypothesis and it is not our purpose to survey the procedures anew rather we suggest in this note that different characteristics of multivariate normality can be examined with different procedures which may thereafter be combined to obtain omnibus tests for the multinormality hypothesis

renormalized differential geometry on path space structural equation curvature abstract the theory of integration in infinite dimensions is in some sense the backbone of probability theory on this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus its first step is the construction at each point of the probability space of a cameron martin like tangent space in which the desired differential calculus can be developed this construction proceeds along the lines of first order differential geometry in this paper we address the following questions what could be the meaning of curvature of the probability space how and why how can curvatures be defined and computed why could a second order differential geometry be relevant to stochastic analysis we try to answer these questions for the probability space associated to the brownian motion of a compact riemannian manifold why a basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature how there are essentially four bottlenecks in the development of differential geometry on wiener riemann manifolds i the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the wiener like measures together with their associated cameron martin like tangent spaces ii the difficulty of finding cylindrical approximations preserving the natural geometrical objects iii the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts iv the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry in the context of path space the ito filtration provides a much richer structure than that available in the framework of an abstract wiener riemann manifold our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames in our context stochastic parallel transport provides a canonical moving frame on the path space the concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems establishing that the riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space those limit theorems are reminiscent of the classical theorems which say that a stratonovich sde is the limit of an appropriate sequence of ode the canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals in this context the anticipative stochastic integral theory of nualart and pardoux will play a decisive role finally the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions in our study we encounter a new type of renormalization thehypoelliptic renormalization which corresponds to the fact that the bracket of smooth vector fields taking their values in the cameron martin space can get out of this cameron martin space this hypoelliptic problem induces the nonrenormalizability of some geometrical objects it leads also to a concept oftangent processesto probability spaces extending that based on the cameron martin theorem for tangent processes a formula of integration by parts still holds furthermore the tangent processes form a lie algebra under the bracket on the other hand tangent processes cannot be stochastically integrated this operation is well defined only for cameron martin type vector fields

some improvements in confidence intervals for standardized regression coefficients yuan and chan psychometrika 76 670 690 2011 doi 10 1007 s11336 011 9224 6 derived consistent confidence intervals for standardized regression coefficients under fixed and random score assumptions jones and waller psychometrika 80 365 378 2015 doi 10 1007 s11336 013 9380 y extended these developments to circumstances where data are non normal by examining confidence intervals based on browne s br j math stat psychol 37 62 83 1984 doi 10 1111 j 2044 8317 1984 tb00789 x asymptotic distribution free adf theory seven different heteroscedastic consistent hc estimators were investigated in the current study as potentially better solutions for constructing confidence intervals on standardized regression coefficients under non normality normal theory adf and hc estimators were evaluated in a monte carlo simulation findings confirmed the superiority of the hc3 mackinnon and white j econ 35 305 325 1985 doi 10 1016 0304 4076 85 90158 7 and hc5 cribari neto and da silva adv stat anal 95 129 146 2011 doi 10 1007 s10182 010 0141 2 interval estimators over jones and waller s adf estimator under all conditions investigated as well as over the normal theory method the hc5 estimator was more robust in a restricted set of conditions over the hc3 estimator some possible extensions of hc estimators to other effect size measures are considered for future developments

bifurcation analysis of magnetic reconnection in hall mhd systems abstract the influence of the hall term on the width of the magnetic islands of the tearing mode is examined we applied the center manifold cmf theory to a magnetohydrodynamic mhd system the mhd system was chosen to be incompressible and includes in addition to viscosity the hall term in ohm s law for certain values of physical parameters the corresponding center manifold is two dimensional and therefore the original partial differential equations could be reduced to a two dimensional system of ordinary ones this amplitude equations exhibit a pitchfork bifurcation which corresponds to the occurrence of the tearing mode eigenvalue problems and linear equations due to the center manifold reduction were solved numerically with the arpack library an important result of this analysis is the growth of the tearing mode island width by increasing the hall parameter a feature which has been observed in recent numerical simulations of collisionless reconnection

regularity criteria for the incompressible hall magnetohydrodynamic equations abstract we establish some new regularity criteria for the three dimensional incompressible hall magnetohydrodynamic equations

a concrete estimate for the weak poincare inequality on loop space the aim of the paper is to study the pinned wiener measure on the loop space over a simply connected compact riemannian manifold together with a hilbert space structure and the ornstein uhlenbeck operator d d we give a concrete estimate for the weak poincare inequality assuming positivity of the ricci curvature of the underlying manifold the order of the rate function is s for any 0

vanishing of one dimensional l 2 cohomologies of loop groups abstract let g be a simply connected compact lie group let l e g be the based loop group with the base point e which is the identity element let e be the pinned brownian motion measure on l e g and let l 2 1 t l e g e d p 1 t l e g e 1 p 2 be a closed 1 form on l e g using results in rough path analysis we prove that there exists a measurable function f on l e g such that d f moreover we prove that dim ker 0 for the hodge kodaira type operator acting on 1 forms on l e g

frame bundle of riemannian path space and ricci tensor in adapted differential geometry abstract the vanishing of the renormalized ricci tensor of the path space above a ricci flat riemannian manifold is discussed

asymptotics of spectral gaps on loop spaces over a class of riemannian manifolds abstract we prove the existence of spectral gaps of ornstein uhlenbeck operators on loop spaces over a class of riemannian manifolds which include hyperbolic spaces this is an alternative proof and an extension of a result in chen et al 13 further we study the asymptotic behavior of the spectral gap

stochastic anticipative integrals on a riemannian manifold we shall use the nualart pardoux approach to the skorohod integral on rd to construct the divergence operator on the path space over a riemannian manifold the cruzeiro malliavin structure equation on the path space is crucial for us to obtain the energy inequality

ito maps and analysis on path spaces we consider versions of malliavin calculus on path spaces of compact manifolds with diffusion measures defining gross sobolev spaces of differentiable functions and proving their intertwining with solution maps mathcal i of certain stochastic differential equations this is shown to shed light on fundamental uniqueness questions for this calculus including uniqueness of the closed derivative operator d and markov uniqueness of the associated dirichlet form a continuity result for the divergence operator by kree and kree is extended to this situation the regularity of conditional expectations of smooth functionals of classical wiener space given mathcal i is considered and shown to have strong implications for these questions a major role is played by the possibly sub riemannian connections induced by stochastic differential equations damped markovian connections are used for the covariant derivatives

an estimate of the gap of spectrum of schrodinger operators which generate hyperbounded semigroups abstract logarithmic sobolev inequalities with potential functions on loop spaces were proved by l gross 1991 j funct anal 102 265 313 s aida 1996 in proceedings of the fifth gregynog symposium stochastic analysis and applications pp 1 19 world scientific singapore and f z gong and z m ma 1998 j funct anal 599 623 the generators of the dirichlet forms are schrodinger operators on loop spaces and they generate hyperbounded semigroups recently f z gong m rockner and l m wu 2000 poincare inequality for weighted first order sobolev spaces on loop spaces submitted proved the existence of the gap of spectrum at the lowest eigenvalue of the schrodinger operators by using m hino s exponential decay estimates of the semigroup 2000 osaka j math 37 603 624 and the author s strong ergodicity property of the semi group s aida 1998 j funct anal 158 152 185 in this paper we will give a lower bound on the gap by using a weak poincare inequality which was introduced by m rockner and f y wang 2000 weak poincare inequalities and l 2 convergence rates of markov semigroups preprint also we will give estimates on the distribution function of ground states using the weak poincare inequality