spiralling self avoiding walks an exact solution an exact solution is presented to a problem of spiralling self avoiding walks on the square lattice recently proposed by privman 1983 for n to infinity the number of n step spiral walks increases as cn approximately 2 23 5 4 pi n 7 4 exp 2 pi n 3 1 2 and their root mean square end to end distance behaves as rn approximately 1 2 square root pi 1n1 2 log n

some nodal properties for a quasilinear differential equation involving the p laplacian abstract in this paper we study a quasilinear differential equation u x p 2 u x w x u x q 2 u x 0 in 0 b where q p 1 a theorem related to some oscillation properties depending on the initial parameters is developed on the basis of this result we also show that the identical zero set of solutions will determine the function w x uniquely under some minor assumption essentially the main methods using in this work are the scaling argument and prufer type substitutions

on estimation of a regression model with long memory stationary errors we consider estimation of a regression model with long memory stationary errors first we estimate the regression parameters by the least squares estimator lse and next those describing the correlation structure of the error terms by using the residuals obtained from the lse certain regularity conditions introduced to develop the asymptotic theory no longer hold in this model in this situation we derive asymptotic properties of the preceding estimation procedure

uniqueness of large solutions abstract given a nondecreasing nonlinearity f we prove uniqueness of large solutions to eq 1 below in the following two cases the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

asymptotic properties of the lse in a regression model with long memory stationary errors we consider asymptotic properties of the least squares estimator lse in a regression model with long memory stationary errors first we derive a necessary and sufficient condition that the lse be asymptotically efficient relative to the best linear unbiased estimator blue then we derive the asymptotic distribution of the lse under a condition on the higher order cumulants of the white noise process of the errors

remarks on uniqueness of boundary blow up solutions abstract we show that there is at most one nonnegative boundary blow up solution for the one dimensional boundary blow up problem u p 2 u f u in 0 1 u 0 u 1 where p 1 provided f c 1 0 c 0 0 with f s 0 and f s 0 for s 0 we see that the same result still holds for some equations with special nonlinearities satisfying f s 0 and f s 0 for s 0 in higher dimensions but we conjecture that the same result should be true for equations with general nonlinearities satisfying f s 0 and f s 0 for s 0 in higher dimensions

critical properties of directed self avoiding walks the generating functions and mean displacements of various two dimensional directed self avoiding walk models are calculated exactly by a simple transfer matrix approach asymptotically the authors find r sub n approximately rn2 1 2 approximately n and rperpendicular to n2 1 approximately n1 2 where n is the number of steps in the walk and and perpendicular to refer to projections of the displacement parallel and perpendicular to the preferred axis of the walk respectively some general properties of directed self avoiding walks for arbitrary dimensions are discussed as well

some convergence results on quadratic forms for random fields and application to empirical covariances limit theorems are proved for quadratic forms of gaussian random fields in presence of long memory we obtain a non central limit theorem under a minimal integrability condition which allows isotropic and anisotropic models we apply our limit theorems and those of ginovian j contemp math anal 34 2 1 15 to obtain the asymptotic behavior of the empirical covariances of gaussian fields which is a particular example of quadratic forms we show that it is possible to obtain a gaussian limit when the spectral density is not in l 2 therefore the dichotomy observed in dimension d 1 between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in d 1

self avoiding path walks on lattices a new universality class the trails problem self avoiding path walks is reconsidered by the conventional series expansion approach an exact enumeration on the square triangular and simple cubic lattices is done by computer up to 18 12 and 11 steps respectively the more self consistent and refined results between the connective constant and the corresponding critical exponent indicate the possibility of there being a different universality class from that of the self avoiding walk an average approach based on stolz s theorem is proposed which often appears to be smoother and better than the traditional one

existence nonexistence and asymptotic behavior of boundary blow up solutions to p x laplacian problems with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u d i v u p x 2 u is called the p x laplacian and x is a singular coefficient the existence and nonexistence of boundary blow up solutions is discussed and the asymptotic behavior of boundary blow up solutions is given in particular we do not assume radial symmetric conditions and the pointwise different exact blow up rate of solutions has been discussed

a test of location for data with slowly decaying serial correlations summary slowly decaying serial correlations have if ignored disastrous effects on classical tests and confidence intervals we propose a modified t test for the location parameter which takes into account such correlations an approximate distribution function of the test statistic is given under the assumption of fractional gaussian noise the results are generalized to prediction intervals for a future average an example is given to illustrate the methods

fractional stochastic differential equations with applications to finance abstract in this paper we use a definition of the fractional stochastic integral given by carmona et al 2003 in 19 and develop a simple approximation method to study quasi linear stochastic differential equations by fractional brownian motion we also propose a stochastic process namely fractional semimartingale to model for the noise driving in some financial models

boundary blow up for differential equations with indefinite weight we obtain results of existence and multiplicity of solutions for the second order equation x q t g x 0 with x t defined for all tis an element of 0 1 and such that x t infinity as t 0 and t 1 we assume g having superlinear growth at infinity and q t possibly changing sign on 0 1 c 2002 elsevier science usa all rights reserved

on the existence of sign changing radial solutions to nonlinear p laplacian equations in rn abstract a class of nonlinear equations r n 1 u p 2 u r n 1 w r f u on 0 1 where 1 p is considered we study the existence of sign changing solutions to this problem some sufficient conditions for such solutions with the prescribed number of zeros are developed we generalize the result of naito and tanaka 2008 to the radial solutions of a class of nonlinear p laplacian equations in r n some related issues on the half line will be also discussed

statistics of spiral lattice site animals with loops for spiral lattice site animals embedded in the square lattice the authors conjecture a relation c c where c is the animal number exponent for animals with c loops 0 is the exponent for trees and is a numerical constant of approximate value 1 62 this result is different from the relation c 0 c which holds true for both undirected and directed animals

boundary blow up solutions in the unit ball asymptotics uniqueness and symmetry abstract we calculate the full asymptotic expansion of boundary blow up solutions see eq 1 below for any nonlinearity f our approach enables us to state sharp qualitative results regarding uniqueness and radial symmetry of solutions as well as a characterization of nonlinearities for which the blow up rate is universal lastly we study in more detail the standard nonlinearities f u u p p 1

asymptotic properties of spiral self avoiding walks the authors consider the spiral self avoiding walk model recently introduced by privman 1983 on the basis of an analogy with the partitioning of the integers they argue that the number of n step spiral walks should increase asymptotically as rho square root n with rho a constant leading to an essential singularity in the generating function enumeration data to 65 terms indicates however that cn apparently varies as rho n alpha with alpha approximately 0 55 they also study the n dependence of the mean square end to end distance rn2 and of the mean rotation angle theta n for n step walks from series extrapolations they estimate that rn2 approximately n1 2 and theta n approximately n0 55

characteristics of deterministic and stochastic sandpile models in a rotational sandpile model rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena in order to study the effect of rotational bias in an out of equilibrium situation like self organized criticality a two state quasideterministic rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains an extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model the probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves the model exhibits characteristics of both deterministic and stochastic sandpile models

large solutions for an elliptic equation with a nonhomogeneous term abstract in this paper we study the elliptic boundary blow up problem u u p 1 u h x in where p 1 is a smooth bounded domain of r n and h c we are concerned with existence and uniqueness of solutions for quite general functions h which may change sign and are not necessarily bounded near

enumeration of directed site animals on two dimensional lattices studies the problem of directed site animals on the square triangular and hexagonal lattices closed form expressions are proposed for a s the number of animals of size s on the square and triangular lattices these expressions have been checked for s or 33 and s or 10 for the square and triangular lattices respectively by explicit enumeration they imply that a s varies as lambda 2 s 0 for large s where lambda 3 for the square lattice and lambda 4 for the triangular and theta 1 2 for both for the hexagonal lattice a s is found for s or 48 the results are consistent with lambda 2 0252 or 0 0005 and theta 1 2

a goodness of fit test for time series with long range dependence we propose a test statistic for goodness of fit in time series with slowly decaying serial correlations the asymptotic distribution of the test statistic originally proposed by milhoj for time series with smooth spectra turns out to be the same under the null hypothesis even if the spectrum has a pole at 0 in particular the test is suitable to detect lack of independence in the observations or estimated residuals if the first few correlations are small but the decay of the correlations is slow

the asymptotic form for the number of spiral self avoiding walks the author investigates the asymptotic behaviour of the number sn of spiral self avoiding walks on the square lattice and show that sn approximately rho square root n with exp pi 312 or rho or exp 2 pi 312

symmetry of large solutions of nonlinear elliptic equations in a ball let g be a locally lipschitz continuous real valued function which satisfies the keller osserman condition and is convex at infinity then any large solution of u g u 0 in a ball is radially symmetric

m estimators of location for gaussian and related processes with slowly decaying serial correlations abstract we investigate the behavior of m estimators of the location parameter for stochastic processes with long range dependence the processes considered are gaussian or one dimensional transformations of gaussian processes it turns out that up to a constant all m estimators are asymptotically equivalent to the arithmetic mean for gaussian processes this constant is always equal to one independently of the function in view of the case of iid observations the results are surprising they are related to earlier work by gastwirth and rubin some simulations illustrate the results

exact multiplicity for boundary blow up solutions abstract the singularly perturbed boundary blow up problem e 2 u u u a 1 u u 0 in b u on b is studied in the unit ball b r n n 2 a 1 2 1 is a constant it is shown that for e 0 sufficiently small there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions

bayesian wavelet based methods for the detection of multiple changes of the long memory parameter long memory processes are widely used in many scientific fields such as economics physics and engineering change point detection problems have received considerable attention in the literature because of their wide range of possible applications here we describe a wavelet based bayesian procedure for the estimation and location of multiple change points in the long memory parameter of gaussian autoregressive fractionally integrated moving average models arfima p d q with unknown autoregressive and moving average parameters our methodology allows the number of change points to be unknown the reversible jump markov chain monte carlo algorithm is used for posterior inference the method also produces estimates of all model parameters performances are evaluated on simulated data and on the benchmark nile river dataset

structure of boundary blow up solutions for quasi linear elliptic problems ii small and intermediate solutions the structure of positive boundary blow up solutions to quasi linear elliptic problems of the form pu f u u on 1 0 in z1 z2 large small and intermediate solutions are obtained for sufficiently large it is known from part i see structure of boundary blow up solutions for quasilinear elliptic problems part i large and small solutions preprint that the large solution is the unique large solution to the problem we will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions our results are new even for the case p 2

multiplicity of positive solutions to boundary blow up elliptic problems with sign changing weights in this paper we consider the elliptic boundary blow up problem u a x ea x upin u on where is a bounded smooth domain of rn a a are positive continuous functions supported in disjoint subdomains of respectively p 1 and e 0 is a parameter we show that there exists e 0 such that no positive solutions exist when e e while a minimal positive solution exists for every e 0 e under the additional hypotheses that and intersect along a smooth n 1 dimensional manifold and a a have a convenient decay near we show that a second positive solution exists for every e 0 e if p n n 2 n 2 our proofs are mainly based on continuation methods

spiral self avoiding walks self avoiding walks with a spiral constraint on the square lattice are enumerated up to 40 steps numerical evidence suggests that they belong to a new universality class

rooted spiral trees in dimensions 2 3 and 4 the authors have studied rooted spiral trees in dimensions 2 3 and 4 by exact enumeration and by monte carlo methods numerical estimates of critical exponents thus obtained support the hypothesis that a dimensional reduction by four occurs in this problem a possible mechanism of the origin of this dimensional reduction is proposed

effect of loops on spiral lattice animal statistics the authors have shown by exact enumeration on a square lattice that spiral lattice site animals and spiral lattice site trees belong to different universality classes i e loops have a non trivial effect on spiral lattice animal statistics this result is contrary to what is known in the cases of undirected and directed lattice animals some special features of spiral lattice animals have been pointed out in this context

second order estimates for large solutions of elliptic equations abstract this paper deals with the second term asymptotic behavior of large solutions to the problems u b x f u x subject to the singular boundary condition u x x where is a smooth bounded domain in r n and b x is a non negative weight function the absorption term f is regularly varying at infinite with index 1 that is lim u f u f u for every 0 and the mapping f u u is increasing on 0 our analysis relies on the karamata regular variation theory

boundary blow up solutions with a spike layer abstract we prove that for large 0 the boundary blow up problem u u u a 1 u in u has a solution with a spike located near the most centered part of our proof is based on the reduction method and uses a cut off technique to avoid the difficulties for the estimates near the boundary of

multiplicity of large solutions for quasi monotone pulse type nonlinearities abstract this paper discusses the keller osserman condition from a dynamical perspective in order to obtain a rather astonishing multiplicity result of large solutions it turns out that for any given increasing positive function f u that satisfies the keller osserman condition destroying the monotonicity of f u on a compact set with arbitrarily small measure can originate an arbitrarily large number of explosive solutions moreover some counterexamples to an important result of 6 are given

the second expansion of large solutions for semilinear elliptic equations abstract in this paper we analyze the influence of the domain geometry in the second expansion of solutions to the boundary blow up elliptic problem u b x f u u 0 x u where is a bounded domain with c 4 smooth boundary in r n b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p p 1

testing for a change of the long memory parameter summary long range dependence is often observed in long time series correlations decay approximately like ik i2 2 with h e 0 5 1 as the lag k tends to infinity the long term features of the data are essentially characterised by the parameter h small changes of h have strong implications for the long term behaviour of the process in particular rates of convergence of estimators for the mean and for many other parameters of interest differ for different values of h for some data sets h appears to change with time in this paper we consider a simple test of the null hypothesis that h is constant the test is based on a functional central limit theorem for quadratic forms critical values for the test statistic are given simulations confirm the validity of the test a data example illustrates its practical application

rooted spiral trees on hyper cubic lattices we study rooted spiral trees in 2 3 and 4 dimensions on a hyper cubic lattice using exact enumeration and monte carlo techniques on the square lattice we also obtain exact lower bound of 1 93565 on the growth constant series expansions give 1 3667 0 0010 and 0 6574 0 0010 on a square lattice with monte carlo simulations we get the estimates as 1 364 0 010 and 0 656 0 010 these results are numerical evidence against earlier proposed dimensional reduction by four in this problem in dimensions higher than two the spiral constraint can be implemented in two ways in either case our series expansion results do not support the proposed dimensional reduction

spiral bond animals ratio approach bond animals with a constraint of a given winding direction on the square lattice are enumerated up to 14 bonds numerical evidence further confirms the previous conjecture using the position space renormalisation group approach that they belong to a new universality class

on boundary blow up solutions to equations involving the laplacian abstract given a non negative continuous function h on r such that h x 0 0 for all x h x t 0 in 0 and h x t non decreasing in t for each x we study the boundary value problem u h x u in u on where r n n 2 is a bounded domain and is the laplacian a degenerate elliptic operator we provide sufficient conditions on h under which the above problem admits a solution or fails to admit a solution a necessary and sufficient condition on f is given for a solution to exist in the special case when h x t b x f t in the latter case an asymptotic boundary behavior of solutions will be studied as an application a sufficient condition on f will be given to ensure the uniqueness of solutions in case b is a constant

large solutions of elliptic semilinear equations in the borderline case an exhaustive and intrinsic point of view abstract we revisit the problem u f u in u x as x where r n n 1 is a bounded smooth domain and f is an increasing and continuous function in r with f 0 0 for which the keller osserman condition holds we study uniqueness of solutions extending known results about the boundary blow up behavior of solutions furthermore we obtain explicit representations for the second order terms in the explosive boundary expansion of solutions under intrinsic and direct assumptions our study is exhaustive including both ordinary and borderline cases providing new and sharp results

testing for homogeneity of variance in time series long memory wavelets and the nile river 1 we consider the problem of testing for homogeneity of variance in a time series with long memorystructure wedemonstratethat atest whose nullhypothesis isdesigned tobewhite noisecan in fact be applied on a scale by scale basis to the discrete wavelet transform of long memory processes in particular we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process the point at which the test statistic using a nondecimated version of the discrete wavelet transform achieves its maximum value can be used to estimate the time of the unknown variance change we apply our proposed test statistic on five time series derived from the historical record of nile river yearly minimum water levels covering 622 1922 a d each series exhibiting various degrees of serial correlation including long memory in the longest subseries spanning 622 1284 a d the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 a d which coincides closely with the construction of a new device around 715 a d for measuring the nile river the test also detects a change in variance for a record of only 36 years index terms 1829 hydrology groundwater hydrology 1869 hydrology stochastic processes 3299 mathematical geophysics general or miscellaneous

testing for change points in time series models and limiting theorems for ned sequences this paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near epoch dependent sequences using these limiting theorems we develop a general asymptotic theory on the wald test for change points in a general class of time series models under the no change point hypothesis as an application we verify our assumptions for the long memory fractional arima model

mackey glass equation driven by fractional brownian motion abstract in this paper we introduce a fractional stochastic version of the mackey glass model which is a potential candidate to model objects in biology and finance by a semi martingale approximate approach we find an semi analytical expression for the solution

on the number of spiral self avoiding walks the authors consider the problem of spiral self avoiding walks as recently introduced by privman 1983 they prove that the number of n step spiral self avoiding walks is given by sn exp 2 pi n 3 12 n74 c 1 o 1 square root n where c pi 4 354 similar results for various subsets of these walks are also obtained

spiralling self avoiding walks self avoiding walks which only step straight ahead or to the left are studied heuristic arguments generating function studies and extrapolation of few step enumerations are described exact asymptotic results are obtained it is found that these spiralling walks are in new universality class wherein the number of n step walks does not behave in a size extensive manner

large solutions for an elliptic system of competitive type existence uniqueness and asymptotic behavior abstract this paper deals with the existence uniqueness and asymptotic behavior of boundary blow up solutions for an elliptic system of competitive type where the weight functions a x b x vanish on the boundary of the underlying domain at different rates according to the point of the boundary the proof relies on subsolutions and supersolutions and the localization method

second order expansion for blowup solutions of semilinear elliptic problems abstract in this paper we mainly study the second order expansion of solutions to the elliptic problems u b x f u u 0 x u where is a bounded domain with a smooth boundary in r n n 2 b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p 1 our analysis is based on the sub supersolution method and karamata regular variation theory

size and shape of directed lattice animals uses position space renormalisation and exact enumeration methods to study configurational properties of directed lattice animals clusters of directed bonds in which the tail of a new bond must be added to the head of existing bonds exponents are found for the divergence of correlation lengths parallel and perpendicular to the preferred axis in addition an exponent is found that characterises the singularity of the directed animal generating function and critical points are located