random strict convexity and random uniform convexity in random normed modules abstract based on the analysis of stratification structure on random normed modules we first present random strict convexity and random uniform convexity in random normed modules then we establish their respective relations to classical strict and uniform convexity in the process some known important results concerning strict convexity and uniform convexity of lebesgue bochner function spaces can be obtained as a special case of our results further we also give their important applications to the theory of random conjugate spaces as well as best approximation finally we conclude this paper with some remarks showing that the study of geometry of random normed modules will also motivate the further study of geometry of probabilistic normed spaces

two fixed point theorems in complete random normed modules and their applications to backward stochastic equations abstract let f f p be a filtered probability space with a filtration f f t t 0 t satisfying the usual conditions and t a finite time l 0 f 0 the algebra of equivalence classes of f 0 measurable real valued random variables on l p f t r d the usual function space and l f 0 p f t r d the l 0 f 0 module generated by l p f t r d the usual backward stochastic equations b s e s are studied for their terminal conditions in l p f t r d motivated by the study of continuous time conditional mean conditional convex risk measure portfolio selection this paper for the first time formulates and studies a more general class of b s e s with their terminal conditions in l f 0 p f t r d the main results of this paper are to prove two fixed point theorems in complete random normed modules which are respectively the random generalizations of banach contraction mapping principle and browder kirk fixed point theorem and give their applications to the general class of b s e s

existence of solutions for impulsive neutral functional differential equations with nonlocal conditions abstract the existence uniqueness and continuous dependence of a mild solution of an impulsive neutral functional differential evolution nonlocal cauchy problem in general banach spaces are studied by using the fixed point technique and semigroup of operators

averaging operators and positive contractive projections abstract the main topic of the present paper is a generalization of two theorems about positive contractive projections on c 0 x due to seever and kelley resp to the more general structure of algebras the theorems in question are the following if a is an archimedean semiprime algebra with the stone condition then every positive contractive projection t in a satisfies the identity t a tb t ta tb for all a b a seever furthermore t is averaging if and only if the range of t is a subalgebra kelley both theorems hold in particular for an archimedean unital algebra in contrast to the original proofs of seever and kelley in the c 0 x case our proofs are purely algebraic and order theoretical

existence results for semilinear differential equations with nonlocal and impulsive conditions abstract this paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions using the techniques of approximate solutions and fixed point existence results are obtained for mild solutions when the impulsive functions are only continuous and the nonlocal item is lipschitz in the space of piecewise continuous functions is not lipschitz and not compact is continuous in the space of bochner integrable functions respectively

conditionally evenly convex sets and evenly quasi convex maps abstract evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces we introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem this notion is then applied to obtain the dual representation of conditionally evenly quasi convex maps which turns out to be a fundamental ingredient in the study of quasi convex dynamic risk measures

weak topologies for modules over rings of bounded random variables abstract in order to establish a functional analytic basis for representation theorems for conditional and multi period risk measures we study locally convex modules over the ring l g their topology is determined by seminorms as expected central mathematical tools of the analysis are hahn banach type and separation theorems which however have to be treated more carefully in the module case once a dual module is introduced one can establish a module version of the bipolar theorem we also prove the krein smulian as well as the alaoglu bourbaki theorem for modules for banach modules their reflexivity is characterized by a compactness criterium in a very weak topology

separation and duality in locally l 0 convex modules motivated by financial applications we study convex analysis for modules over the ordered ring l0 of random variables we establish a module analogue of locally convex vector spaces namely locally l0 convex modules in this context we prove hyperplane separation theorems we investigate continuity subdifferentiability and dual representations of fenchel moreau type for l0 convex functions from l0 modules into l0 several examples and applications are given

exact results for the asymmetric simple exclusion process with a blockage we present new results for the current as a function of transmission rate in the one dimensional totally asymmetric simple exclusion process tasep with a blockage that lowers the jump rate at one site from one tor 1 exact finitevolume results serve to bound the allowed values for the current in the infinite system this proves the existence of a nonequilibrium phase transition corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state a series expansion inr derived from the finite systems is proven to be asymptotic for all sufficiently large systems pade approximants based on this series which make specific assumptions about the nature of the singularity atr 1 match numerical data for the infinite system to 1 part in 104

existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α norm abstract this paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the norm the linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators and the nonlinear part satisfies some lipschitz conditions with respect to the norm by using a fixed point theorem of sadovskii we establish some existence results which generalize the recent conclusions on this issue in the end the obtained results will be applied to a class of partial differential equations with nonlocal conditions

the algebraic structure of finitely generated l0 f k modules and the helly theorem in random normed modules abstract let k be the scalar field of real numbers or complex numbers and l 0 f k the algebra of equivalence classes of k valued random variables defined on a probability space f p in this paper we first characterize the algebraic structure of finitely generated l 0 f k modules and then combining the recently developed separation theorem in random locally convex modules we prove the helly theorem in random normed modules with the countable concatenation property under the framework of random conjugate spaces at the same time a simple counterexample shows that it is necessary to require the countable concatenation property

the hajek renyi chow maximal inequality and a strong law of large numbers in riesz spaces abstract in this paper we generalize the hajek renyi chow maximal inequality for submartingales to l p type riesz spaces with conditional expectation operators as applications we obtain a submartingale convergence theorem and a strong law of large numbers in riesz spaces along the way we develop a riesz space variant of the clarkson s inequality for 1 p 2

limiting curves for i i d records we consider the concentration of measure for n i i d two dimensional random variables under the conditioning that they form a record under mild conditions we show that all random variables tend to concentrate as n rightarrow infty around limiting curves which are the solutions of an appropriate variational problem we also show that the same phenomenon occurs without the records conditioning for the longest increasing subsequence in the sample

conditional expectations on riesz spaces abstract conditional expectations operators acting on riesz spaces are shown to commute with a class of principal band projections using the above commutation property conditional expectation operators on riesz spaces are shown to be averaging operators here the theory of f algebras is used when defining multiplication on the riesz spaces this leads to the extension of these conditional expectation operators to their so called natural domains i e maximal domains for which the operators are both averaging operators and conditional expectations the natural domain is in many aspects analogous to l 1

near epoch dependence in riesz spaces abstract the abstraction of the study of stochastic processes to banach lattices and vector lattices has received much attention by grobler kuo labuschagne stoica troitsky and watson over the past fifteen years by contrast mixing processes have received very little attention in particular mixingales were generalized to the riesz space setting in kuo et al 2013 12 the concepts of strong and uniform mixing as well as related mixing inequalities were extended to this setting in kuo et al 2017 11 in the present work we formulate the concept of near epoch dependence for riesz space processes and show that if a process is near epoch dependent and either strong or uniform mixing then the process is a mixingale giving access to a law of large numbers the above is applied to autoregressive processes of order 1 in riesz spaces

a note on the diffusion of directed polymers in a random environment a simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford 3 and if the disorder is small enough this simplifies and extends an approach by j imbrie and t spencer

limiting shape for directed percolation models we consider directed first passage and last passage percolation on the nonnegative lattice z d d 2 with i i d weights at the vertices under certain moment conditions on the common distribution of the weights the limits g x lim n n 1 t nx exist and are constant a s for x r d where t z is the passage time from the origin to the vertex z z d we show that this shape function g is continuous on r d in particular at the boundaries in two dimensions we give more precise asymptotics for the behavior of g near the boundaries these asymptotics depend on the common weight distribution only through its mean and variance in addition we discuss growth models which are naturally associated to the percolation processes giving a shape theorem and illustrating various possible types of behavior with output from simulations

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

limit laws for martingales in vector lattices abstract we prove limit laws for martingales in vector lattices under suitable technical hypotheses involving the increments of the sequences therein

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

directed last passage percolation with discontinuous weights we prove that a directed last passage percolation model with discontinuous macroscopic non random inhomogeneities has a continuum limit that corresponds to solving a hamilton jacobi equation in the viscosity sense this hamilton jacobi equation is closely related to the conservation law for the hydrodynamic limit of the totally asymmetric simple exclusion process we also prove convergence of a numerical scheme for the hamilton jacobi equation and present an algorithm based on dynamic programming for finding the asymptotic shapes of maximal directed paths

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

on a new class of abstract integral equations and applications abstract in this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

asymptotic results on infinite tandem queueing networks we consider an infinite tandem queueing network consisting of gi 1 stations with i i d service times we investigate the asymptotic behavior of t n k the inter arrival times between customers n and n 1 at station k and that of w n k the waiting time of customer n at station k we establish a duality property by which w n k and the idle times y n k play symmetrical roles this duality structure interesting by itself is also instrumental in proving some of the ergodic results we consider two versions of the model the quadrant and the half plane in the quadrant version the sequences of boundary conditions w 0 k k and t n 0 n are given in the half plane version the sequence t n 0 n is given under appropriate assumptions on the boundary conditions and on the services we obtain ergodic results for both versions of the model for the quadrant version we prove the existence of temporally ergodic evolutions and of spatially ergodic ones furthermore the process t n k n converges weakly with k to a limiting distribution which is invariant for the queueing operator in the more difficult half plane problem the aim is to obtain evolutions which are both temporally and spatially ergodic we prove that 1 n k 1 nw 0 k converges almost surely and in l1 to a finite constant this constitutes a first step in trying to prove that t n k n converges weakly with k to an invariant limiting distribution

scaling limit for the space time covariance of the stationary totally asymmetric simple exclusion process the totally asymmetric simple exclusion process tasep on the one dimensional lattice with the bernoulli measure as initial conditions 0 1 is stationary in space and time let nt j be the number of particles which have crossed the bond from j to j 1 during the time span 0 t for open image in new window we prove that the fluctuations of nt j for large t are of order t1 3 and we determine the limiting distribution function open image in new window which is a generalization of the gue tracy widom distribution the family open image in new window of distribution functions have been obtained before by baik and rains in the context of the png model with boundary sources which requires the asymptotics of a riemann hilbert problem in our work we arrive at open image in new window through the asymptotics of a fredholm determinant open image in new window is simply related to the scaling function for the space time covariance of the stationary tasep equivalently to the asymptotic transition probability of a single second class particle

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

on in dependence measures in riesz spaces abstract in this paper we introduce an independence measure between a vector f in a riesz space e and a conditional expectation operator t on e we show that this measure satisfies some postulates corresponding to these formulated by renyi 1959 for dependence measure between random variables the resulting dependence measure in e is also investigated some examples of application are given

equilibrium pricing in incomplete markets under translation invariant preferences we propose a general discrete time framework for deriving equilibrium prices of financial securities it allows for heterogeneous agents unspanned random endowments and convex trading constraints we give a dual characterization of equilibria and provide general results on their existence and uniqueness in the special case where all agents have preferences of the same type and in equilibrium all random endowments are replicable by trading in the financial market we show that a one fund theorem holds and give an explicit expression for the equilibrium pricing kernel

ekelandʼs variational principle for an l 0 valued function on a complete random metric space abstract motivated by the recent work on conditional risk measures this paper studies the ekeland s variational principle for a proper lower semicontinuous and lower bounded l 0 valued function where l 0 is the set of equivalence classes of extended real valued random variables on a probability space first we prove a general form of ekeland s variational principle for such a function defined on a complete random metric space then we give a more precise form of ekeland s variational principle for such a local function on a complete random normed module finally as applications we establish the bishop phelps theorem in a complete random normed module under the framework of random conjugate spaces

conditional lp spaces and the duality of modules over f algebras abstract motivated by dynamic asset pricing we extend the dual pairs theory of dieudonne 1942 and mackey 1945 to pairs of modules over a dedekind complete f algebra with multiplicative unit the main tools are a hahn banach theorem for modules of this kind a topology on the f algebra that has the special feature of coinciding with the norm topology when the algebra is a banach algebra and with the strong order topology of filipovic kupper and vogelpoth 2009 when the algebra of all random variables on a probability space g p is considered as a leading example we study in some detail the duality of conditional l p spaces

mixing inequalities in riesz spaces abstract various topics in stochastic processes have been considered in the abstract setting of riesz spaces for example martingales martingale convergence ergodic theory amarts markov processes and mixingales here we continue the relaxation of conditional independence begun in the study of mixingales and study mixing processes the two mixing coefficients which will be considered are the strong and uniform mixing coefficients we conclude with mixing inequalities for these types of processes in order to facilitate this development the study of generalized l 1 and l spaces begun by kuo labuschagne and watson will be extended

spaces of regular abstract martingales abstract in 15 10 the authors introduced and studied the space m r of regular martingales on a vector lattice and the space m r of bounded regular martingales on a banach lattice in this note we study these two spaces from the vector lattice point of view we show in particular that these spaces need not be vector lattices however if the underlying space is order complete then m r is a vector lattice and m r is a banach lattice under the regular norm

numerical schemes and rates of convergence for the hamilton jacobi equation continuum limit of nondominated sorting non dominated sorting arranges a set of points in n dimensional euclidean space into layers by repeatedly removing the coordinatewise minimal elements it was recently shown that nondominated sorting of random points has a hamilton jacobi equation continuum limit the obvious numerical scheme for this pde has a slow convergence rate of o h frac 1 n o h1n in this paper we introduce two new numerical schemes that have formal rates of o h and we prove the usual o sqrt h o h theoretical rates we also present the results of numerical simulations illustrating the difference between the formal and theoretical rates

existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators abstract this paper is mainly concerned with existence of mild solutions for a first order impulsive neutral integrodifferential inclusions with nonlocal initial conditions in norm we assume that the linear part generates an analytic semigroup and transform it into an integral inclusion by using a fixed point theorem for multi valued maps due to dhage a main existence theorem is established finally we present an example to illustrate this main theorem

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

stability in locally l0 convex modules and a conditional version of james compactness theorem abstract locally l 0 convex modules were introduced in filipovic et al 2009 10 as the analytic basis for the study of conditional risk measures later the algebra of conditional sets was introduced in drapeau et al 2016 8 in this paper we study locally l 0 convex modules and find exactly which subclass of locally l 0 convex modules can be identified with the class of locally convex vector spaces within the context of conditional set theory second we provide a version of the classical james theorem of characterization of weak compactness for conditional banach spaces finally we state a conditional version of the fatou and lebesgue properties for conditional convex risk measures and as application of the developed theory we establish a version of the so called jouini schachermayer touzi theorem for robust representation of conditional convex risk measures defined on a l type module

airy kernel with two sets of parameters in directed percolation and random matrix theory we introduce a generalization of the extended airy kernel with two sets of real parameters we show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

a pde based approach to nondominated sorting nondominated sorting is a fundamental combinatorial problem in multiobjective optimization and is equivalent to the longest chain problem in combinatorics and random growth models for crystals in materials science in a previous work siam j math anal 46 2014 pp 603 638 we showed that nondominated sorting has a continuum limit that corresponds to solving a hamilton jacobi equation in this work we present and analyze a fast numerical scheme for this hamilton jacobi equation and show how it can be used to design a fast algorithm for approximate nondominated sorting

current fluctuations for tasep a proof of the prahofer spohn conjecture we consider the family of two sided bernoulli initial conditions for tasep which as the left and right densities p are varied give rise to shock waves and rarefaction fans the two phenomena which are typical to tasep we provide a proof of conjecture 7 1 of progr probab 51 2002 185 204 which characterizes the order of and scaling functions for the fluctuations of the height function of two sided tasep in terms of the two densities and the speed y around which the height is observed in proving this theorem for tasep we also prove a fluctuation theorem for a class of comer growth processes with external sources or equivalently for the last passage time in a directed last passage percolation model with two sided boundary conditions and 1 p we provide a complete characterization of the order of and the scaling functions for the fluctuations of this model s last passage time l n m as a function of three parameters the two boundary source rates p and 1 p and the scaling ratio y 2 m n the proof of this theorem draws on the results of comm math phys 265 2006 1 44 and extensively on the work of ann probab 33 2005 1643 1697 on finite rank perturbations of wishart ensembles in random matrix theory

existence uniqueness and regularity of solutions to semilinear nonlocal functional differential problems abstract in this paper we consider a semilinear nonlocal functional differential problem in a banach space we first establish the existence uniqueness and continuation of a mild solution we then prove some regularity results for this mild solution under different conditions finally we consider some applications of the abstract results

existence and uniqueness of mild solution of time fractional semilinear differential equations with a nonlocal final condition abstract in this paper we investigate a time fractional semilinear differential equation with final nonlocal condition u x t g u x j 1 m j u x t j under some assumptions we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions the results are based on some fixed point theorems two examples are presented to illustrate our results

limit processes for tasep with shocks and rarefaction fans we consider the totally asymmetric simple exclusion process tasep with two sided bernoulli initial condition i e with left density and right density we study the associated height function whose discrete gradient is given by the particle occurrences macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of we characterize the large time scaling limit of the multipoint fluctuations as a function of the densities and of the different macroscopic regions moreover using a slow decorrelation phenomena the results are extended from fixed time to the whole space time except along the some directions the characteristic solutions of the related burgers equation where the problem is still open

mixingales on riesz spaces abstract a mixingale is a stochastic process which combines properties of martingales and mixing sequences mcleish introduced the term mixingale at the 4th conference on stochastic processes and application at york university toronto 1974 in the context of l 2 in this paper we generalize the concept of a mixingale to the measure free riesz space setting this generalizes all of the l p 1 p variants and prove that a weak law of large numbers holds for riesz space mixingales in the process we also generalize the concept of uniform integrability to the riesz space setting

relations between some basic results derived from two kinds of topologies for a random locally convex module the purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies namely the e topology and the stronger locally l0 convex topology for a random locally convex module first we give an extremely simple proof of the known hahn banach extension theorem for l0 linear functions as well as its continuous variant then we give the relations between the hyperplane separation theorems in d filipovic m kupper n vogelpoth separation and duality in locally l0 convex modules j funct anal 256 2009 3996 4029 and a basic strict separation theorem in t x guo h x xiao x x chen a basic strict separation theorem in random locally convex modules nonlinear anal 71 2009 3794 3804 in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies as applications of the fact we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the e topology are still valid under the locally l0 convex topology which considerably enriches financial applications of random normed modules

a direct verification argument for the hamilton jacobi equation continuum limit of nondominated sorting abstract nondominated sorting is a combinatorial algorithm that sorts points in euclidean space into layers according to a partial order it was recently shown that nondominated sorting of random points has a hamilton jacobi equation continuum limit the original proof given in calder et al 2014 relies on a continuum variational problem in this paper we give a new proof using a direct verification argument that completely avoids the variational interpretation we believe this may be generalized to apply to other stochastic homogenization problems for which there is no obvious underlying variational principle

the ito integral for brownian motion in vector lattices part 2 abstract the ito integral for brownian motion in a vector lattice as constructed in part 1 of this paper is extended to accommodate a larger class of integrands this extension provides an analogue of the indefinite ito integral in the classical setting which yields a local martingale the assumption is that there exists a conditional expectation operator on the vector lattice and the construction does not depend on a probability measure space the classical case of the extended ito integral is a special case of the constructed integral in the vector lattice

existence of solutions for a class of abstract differential equations with nonlocal conditions abstract we discuss the existence of mild classical and strict solutions for a class of abstract differential equations with nonlocal conditions our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution some concrete applications to partial differential equations are considered

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

orthogonal decompositions in hilbert a modules abstract pre hilbert a modules are a natural generalization of inner product spaces in which the scalars are allowed to be from an arbitrary algebra in this perspective submodules are the generalization of vector subspaces the notion of orthogonality generalizes in an obvious way too in this paper we focus on f algebras a that are either of l or of l 0 type we provide necessary and sufficient topological conditions for a submodule to be orthogonally complemented then we present four applications of our results the most important ones are doob s and kunita watanabe s decompositions for conditionally square integrable processes they are obtained as orthogonal decomposition results carried out in an opportune pre hilbert a module second we show that a version of stricker s lemma can be also derived as a corollary of our results finally we provide a version of the koopman von neumann decomposition theorem for a specific pre hilbert module which is useful in ergodic theory

the mean ergodic theorem on random reflexive random normed modules in this paper we prove a mean ergodic theorem for an almost surely power bounded random linear operator on a random reflexive random normed module which general izes and improves several known important results

a unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time in this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures also known as acceptability indices the proposed framework not only integrates existing forms of time consistency but also provides a comprehensive toolbox for analysis and synthesis of the concept of time consistency in decision making in particular it allows for in depth comparative analysis of most of the existing types of time consistency a feat that has not been possible before and which is done in the companion paper by the authors in our approach the time consistency is studied for a large class of maps that are postulated to satisfy only two properties monotonicity and locality we call these maps lm measures the time consistency is defined in terms of an update rule the form of the update rule introduced here is novel and is perfectly suited for developing the unifying framework that is worked out in this paper as an illustration of the applicabi

the algebra of conditional sets and the concepts of conditional topology and compactness abstract the concepts of a conditional set a conditional inclusion relation and a conditional cartesian product are introduced the resulting conditional set theory is sufficiently rich in order to construct a conditional topology a conditional real and functional analysis indicating the possibility of a mathematical discourse based on conditional sets it is proved that the conditional power set is a complete boolean algebra and a conditional version of the axiom of choice the ultrafilter lemma tychonoff s theorem the borel lebesgue theorem the hahn banach theorem the banach alaoglu theorem and the krein smulian theorem are shown

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process

hilbert a modules abstract we consider real pre hilbert modules h on archimedean f algebras a with unit e we provide conditions on a and h such that a riesz representation theorem for bounded continuous a linear operators holds