the dominguez lorenzo condition and multivalued nonexpansive mappings abstract let e be a nonempty bounded closed convex separable subset of a reflexive banach space x which satisfies the dominguez lorenzo condition i e an inequality concerning the asymptotic radius of a sequence and the chebyshev radius of its asymptotic center we prove that a multivalued nonexpansive mapping t e 2 x which is compact convex valued and such that t e is bounded and satisfies an inwardness condition has a fixed point as a consequence we obtain a fixed point theorem for multivalued nonexpansive mappings in uniformly nonsquare banach spaces which satisfy the property worth extending a known result for the case of nonexpansive single valued mappings we also prove a common fixed point theorem for two nonexpansive commuting mappings t e e and t e kc e where kc e denotes the class of all compact convex subsets of e when x is a uniformly convex banach space

a local limit theorem for random walks conditioned to stay positive we consider a real random walk s n x1 x n attracted without centering to the normal law this means that for a suitable norming sequence a n we have the weak convergence s n a n x dx x being the standard normal density a local refinement of this convergence is provided by gnedenko s and stone s local limit theorems in the lattice and nonlattice case respectively now let open image in new window denote the event s1 0 s n 0 and let s n denote the random variable s n conditioned on open image in new window it is known that s n a n x dx where x x exp x2 2 1 x 0 what we establish in this paper is an equivalent of gnedenko s and stone s local limit theorems for this weak convergence we also consider the particular case when x1 has an absolutely continuous law in this case the uniform convergence of the density of s n a n towards x holds under a standard additional hypothesis in analogy to the classical case we finally discuss an application of our main results to the asymptotic behavior of the joint renewal measure of the ladder variables process unlike the classical proofs of the llt we make no use of characteristic functions our techniques are rather taken from the so called fluctuation theory for random walks

one sided local large deviation and renewal theorems in the case of infinite mean if s n n 0 is an integer valued random walk such that s n a n converges in distribution to a stable law of index 0 1 as n then gnedenko s local limit theorem provides a useful estimate for p s n r for values of r such that r a n is bounded the main point of this paper is to show that under certain circumstances there is another estimate which is valid when r a n in other words to establish a large deviation local limit theorem we also give an asymptotic bound for p s n r which is valid under weaker assumptions this last result is then used in establishing some local versions of generalized renewal theorems

random walks in cones we study the asymptotic behavior of a multidimensional random walk in a general cone we find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone the main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments for the proof of tail asymptotics and integral limit theorems we use a strong approximation of random walks by brownian motion for the proof of local limit theorems we suggest a rather simple approach which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks we also discuss some possible applications of our results to ordered random walks and lattice path enumeration

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

subcritical percolation with a line of defects we consider the bernoulli bond percolation process pp p on the nearest neighbor edges of zd which are open independently with probability p pc except for those lying on the first coordinate axis for which this probability is p define p p limn n 1logpp p 0 ne1 and p p p we show that there exists p c p c p d such that p p p if p p c moreover p c p 2 p c p 3 p and p c p d p for d 4 we also analyze the behavior of p p p as p p c in dimensions d 2 3 finally we prove that when p p c the following purely exponential asymptotics holds pp p 0 ne1 de p p n 1 o 1 for some constant d d p p uniformly for large values of n this work gives the first results on the rigorous analysis of pinning type problems that go beyond the effective models and don t rely on exact computations

edelstein s method and fixed point theorems for some generalized nonexpansive mappings abstract a new condition for mappings called condition c which is more general than nonexpansiveness was recently introduced by suzuki t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 following the idea of kirk and massa theorem in w a kirk s massa remarks on asymptotic and chebyshev centers houston j math 16 1990 364 375 we prove a fixed point theorem for mappings with condition c on a banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact this covers a result obtained by suzuki t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 we also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of banach spaces satisfying property d consequently we extend the results in t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 to many other banach spaces

fuzzy set connectives as combinations of belief structures abstract consonant belief structures provide a representation for fuzzy sets owing to the fact that their plausibility measures are essentially possibility measures we note that two belief structures are equivalent if their plausibility and belief functions are equal this observation leads us to provide a multiple number of equivalent representations for any belief structure commensurate representations can be induced for two different belief structures by forcing the same number of focal elements with the same weights we show that if we represent two consonant belief structures in a commensurate manner then their aggregations are closed with respect to consonance provided that the additional requirement that the underlying probability distributions satisfy a condition of correlation is imposed the results of this work allow us to use belief structure representations for the manipulation of fuzzy subsets under various logical combinations all basic fuzzy set connectives can thus be interpreted in the framework of the theory of evidence

the jordan von neumann constants and fixed points for multivalued nonexpansive mappings the purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of banach spaces furthermore we demonstrate a relationship between the weakly convergent sequence coefficient wcs x and the jordan von neumann constant cnj x of a banach space x using this fact we prove that if cnj x is less than an appropriate positive number then every multivalued nonexpansive mapping t e kc e has a fixed point where e is a nonempty weakly compact convex subset of a banach space x and kc e is the class of all nonempty compact convex subsets of e

on the joint distribution of ladder variables of random walk the ladder timen and ladder heighth of a random walk s n n 1 as a pair n h lie in the domain of attraction of a bivariate stable law ifs1 is in a domain of attraction as was shown by greenwood et al 1982 in this paper we prove a converse ifp s n 0 converges and n h lies in a bivariate domain of attraction thens1 is also in a domain of attraction

conditioned limit theorems for products of random matrices consider the product g n g n dots g 1 of the random matrices g 1 dots g n in gl left d mathbb r right and the random process g n v g n dots g 1 v in mathbb r d starting at point v in mathbb r d smallsetminus left 0 right it is well known that under appropriate assumptions the sequence left log left vert g n v right vert right n geq 1 behaves like a sum of i i d r v s and satisfies standard classical properties such as the law of large numbers law of iterated logarithm and the central limit theorem denote by mathbb b the closed unit ball in mathbb r d and by mathbb b c its complement for any v in mathbb b c define the exit time of the random process g n v from mathbb b c by tau v min left n geq 1 g n v in mathbb b right we establish the asymptotic as n rightarrow infty of the probability of the event left tau v n right and find the limit law for the quantity frac 1 sqrt n log left vert g n v right vert conditioned that tau v n

a matrix method of basic belief assignment s negation in dempster shafer theory negation is a new perspective to represent knowledge the negation of probability distribution has been proposed and it has a lot of interesting properties which can reach a maximum entropy because of the defects of the classical probability theory in the expression of uncertainty the basic belief assignment bba in the dempster shafer theory d s theory are widely used in decision theory thus negation provides a new perspective for d s theory to measure fuzziness in this paper a new definition of negation of bba is presented in the proposed negation bbas are represented as vectors and negation is realized by matrix operators this method has a good interpretation of the matrix operators and has the merit of simplifying the problem with several different definitions of entropy to determinate the uncertainty of bba the proposed negation of bba can reach a maximum belief entropy when the entropies satisfy a certain property

limit theorems for random walks conditioned to stay positive let s n be a random walk on the integers with negative drift and let a n s k geq 0 1 leq k leq n and a a infty conditioning on a is troublesome because p a 0 and there is no natural sigma field of events like a a natural definition of p b mid a is lim n rightarrow infty p b mid a n the main result here shows that this definition makes sense at least for a large class of events b the finite dimensional conditional distributions for the process s k k geq 0 given a n converge strongly to the finite dimensional distributions for a measure mathbf q this distribution mathbf q is identified as the distribution for a stationary markov chain on 0 1 ldots

remarks on sufficient conditions for fixed points of multivalued nonexpansive mappings abstract in recent papers s dhompongsa t dominguez benavides a kaewcharoen a kaewkhao b panyanak the jordan von neumann constants and fixed points for multivalued nonexpansive mappings j math anal appl 320 2006 916 927 s dhompongsa a kaewcharoen a kaewkhao the dominguez lorenzo condition and multivalued nonexpansive mappings nonlinear anal 64 2006 958 970 two sufficient conditions namely the dominguez lorenzo condition and property d for fixed points of multivalued nonexpansive mappings are introduced the authors also give some sufficient conditions for the dominguez lorenzo condition and property d in their proofs it seems reasonable to use the james and von neumann jordan constants with slight modifications significant improvements are obtained some new estimates are tight in hilbert spaces

harmonic renewal measures and bivariate domains of attraction in fluctuation theory each probability measure c on a first orthant is associated with a harmonic renewal measure g specifically we consider n s n the ladder time place of a random walk sn using bivariate g we show that when s1 is in a domain of attraction so is n sn this unifies and generalizes results of sinai rogosin

an evidential fusion approach for gender profiling cctv closed circuit television systems are broadly deployed in the present world to ensure in time reaction for intelligent surveillance it is a fundamental task for real world applications to determine the gender of people of interest however normal video algorithms for gender profiling usually face profiling have three drawbacks first the profiling result is always uncertain second the profiling result is not stable the degree of certainty usually varies over time sometimes even to the extent that a male is classified as a female and vice versa third for a robust profiling result in cases that a person s face is not visible other features such as body shape are required these algorithms may provide different recognition results at the very least they will provide different degrees of certainties to overcome these problems in this paper we introduce an dempster shafer ds evidential approach that makes use of profiling results from multiple algorithms over a period of time in particular denoeux s cautious rule is applied for fusing mass functions through time lines experiments show that this approach does provide better results than single profiling results and classic fusion results furthermore it is found that if severe mis classification has occurred at the beginning of the time line the combination can yield undesirable results to remedy this weakness we further propose three extensions to the evidential approach proposed above incorporating notions of time window time attenuation and time discounting respectively these extensions also applies denoeux s rule along with time lines and take the ds approach as a special case experiments show that these three extensions do provide better results than their predecessor when mis classifications occur

spitzer s condition and ladder variables in random walks spitzer s condition holds for a random walk if the probabilities n p n 0 converge in cesaro mean to where 0 1 we answer a question which was posed both by spitzer 12 and by emery 5 by showing that whenever this happens it is actually true that n converges to this also enables us to give an improved version of a result in doney and greenwood 4 and show that the random walk is in a domain of attraction without centering if and only if the first ladder epoch and height are in a bivariate domain of attraction

conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence dempster s rule plays a central role in the theory of belief functions however it assumes the combined bodies of evidence to be distinct an assumption which is not always verified in practice in this paper a new operator the cautious rule of combination is introduced this operator is commutative associative and idempotent this latter property makes it suitable to combine belief functions induced by reliable but possibly overlapping bodies of evidence a dual operator the bold disjunctive rule is also introduced this operator is also commutative associative and idempotent and can be used to combine belief functions issues from possibly overlapping and unreliable sources finally the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

the james constant the jordan von neumann constant weak orthogonality and fixed points for multivalued mappings abstract we give some sufficient conditions for the dominguez lorenzo condition in terms of the james constant the jordan von neumann constant and the coefficient of weak orthogonality as a consequence we obtain fixed point theorems for multivalued nonexpansive mappings

the fixed point property for multivalued nonexpansive mappings we show some properties concerning geometrical constants of banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties

conditioned local limit theorems for random walks defined on finite markov chains let x n n geqslant 0 be a markov chain with values in a finite state space mathbb x starting at x 0 x in mathbb x and let f be a real function defined on mathbb x set s n sum k 1 n f x k n geqslant 1 for any y in mathbb r denote by tau y the first time when y s n becomes non positive we study the asymptotic behaviour of the probability mathbb p x left y s n in z z a tau y n right as n rightarrow infty we first establish for this probability a conditional version of the local limit theorem of stone then we find for it an asymptotic equivalent of order n 3 2 and give a generalization which is useful in applications we also describe the asymptotic behaviour of the probability mathbb p x left tau y n right as n rightarrow infty

banach space properties sufficient for normal structure in this paper we establish lower bounds for the weakly convergent sequence coefficient wcs x of a banach space x in terms of some well known moduli and coefficients by mean of these bounds we identify several properties of geometrical nature which imply normal structure we show that these properties are strictly more general than other previously known sufficient conditions for normal structure

local probabilities for random walks conditioned to stay positive let s0 0 sn n 1 be a random walk generated by a sequence of i i d random variables x1 x2 and let tau rm min n geq 1 s n leq 0 and tau rm min n geq1 s n 0 assuming that the distribution of x1 belongs to the domain of attraction of an stable law we study the asymptotic behavior as n rightarrow infty of the local probabilities bf p tau pm n and prove the gnedenko and stone type conditional local limit theorems for the probabilities bf p s n in x x delta tau n with fixed and x x n in 0 infty

banach ultrapowers and multivalued nonexpansive mappings the banach ultrapower construction is applied in fixed point theory for multivalued mappings we introduce the notion of ultra asymptotic centers and use it to remove the separability assumption from the results of dominguez benavides lorenzo ramirez 2004 and dhompongsa kaewcharoen kaewkhao 2006

some geometric conditions which imply the fixed point property for multivalued nonexpansive mappings abstract we show some geometric conditions on a banach space x concerning the modulus of smoothness the coefficient of weak orthogonality the coefficient r a x the james constant and the jordan von neumann constant which imply the existence of fixed points for multivalued nonexpansive mappings these fixed point theorems improve some previous results and give affirmative answers to some open questions