bluuebunny/crossref_metadata_2025 huggingface dataset:
Progestin-Inflammatory Cytokine Interactions Affect Matrix Metalloproteinase-1 and -3 Expression in Term Decidual Cells: Implications for Treatment of Chorioamnionitis-Induced Preterm Delivery
Authors: Oner Ceyda , Schatz Frederick , Kizilay Gulnur , Murk William , Buchwalder Lynn F. , Kayisli Umit A. , Arici Aydin , Lockwood Charles J.
Published: October 2007

Context: Chorioamnionitis (CAM)-elicited preterm delivery (PTD) is associated with elevated amniotic fluid levels of IL-1β and TNF-α. We hypothesized that IL-1β and TNF-α may induce matrix metalloproteinase (MMP)-1 and MMP-3 activity to promote PTD by degrading decidual and fetal membranes and cervical extracellular matrix.

Objective: Our objective was to evaluate: 1) MMP-1 and MMP-3 expression in decidual sections from uncomplicated term, idiopathic preterm, and CAM-complicated deliveries, and 2) the separate and interactive effects of IL-1β, TNF-α, medroxyprogesterone acetate (MPA), and a p38 MAPK inhibitor (SB203580) on MMP-1 and MMP-3 expression in term decidual cells (DCs).

Interventions and Main Outcome Measures: Decidua were immunostained for MMP-1 and MMP-3. Cultured term DCs were incubated with estradiol (E2) or E2 plus MPA with or without IL-1β or TNF-α with or without SB203580. ELISA and Western blotting assessed secreted MMP-1 and MMP-3 levels, quantitative real-time RT-PCR assessed mRNA levels, and substrate gel zymography was used to determined MMP-1 and MMP-3 proteolytic activity.

Results: MMP-1 and MMP-3 immunostaining was more prominent in CAM-complicated decidua vs. control preterm and term decidual specimens (P < 0.05). Compared with basal outputs by DCs incubated with E2, TNF-α enhanced MMP-1 and MMP-3 secretion by 14 ± 3- and 9 ± 2-fold, respectively, and IL-1β increased MMP-1 and MMP-3 secretion by 13 ± 3- and 19 ± 2-fold, respectively (P < 0.05). Addition of MPA lowered basal MMP-1 and MMP-3 outputs by 70%, whereas the TNF-α- and IL-1β-enhanced MMP-1 and MMP-3 levels were blunted by more than 50% (P < 0.05). SB203580 suppressed TNF-α- and IL-1β-induced MMP-1 and MMP-3 secretion by severalfold. Western blotting confirmed the ELISA results, and mRNA levels corresponded with MMP-1 and MMP-3 protein levels. MMP-1 and MMP-3 proteolytic activity was confirmed by substrate gel zymography.

Conclusion: Augmented DC-expressed MMP-1 and MMP-3 in CAM-complicated pregnancies may promote PTD via decidual, fetal membrane, and cervical extracellular matrix degradation. Effects of progestin-p38 MAPK signaling inhibition on cytokine-enhanced MMP-1 and MMP-3 expression in term DCs suggest alternative mechanisms to prevent CAM-induced PTD.
Type 1 Diabetes Associated with Acquired Generalized Lipodystrophy and Insulin Resistance: The Effect of Long-Term Leptin Therapy
Authors: Park Jean Y. , Chong Angeline Y. , Cochran Elaine K. , Kleiner David E. , Haller Michael J. , Schatz Desmond A. , Gorden Phillip
Published: October 2007

Context: Acquired generalized lipodystrophy (AGL) is marked by severe insulin resistance and hypertriglyceridemia. Rarely, AGL and type 1 diabetes (T1D) coexist.

Objective: Our objective was to describe the response to leptin therapy in patients with coexisting AGL and T1D and to document the autoimmune diseases associated with AGL.

Design and Setting: We conducted an open-label prospective study at the Clinical Research Center of the National Institutes of Health.

Patients: Participants included 50 patients with generalized or partial lipodystrophy (acquired or congenital); two patients had both AGL and T1D.

Intervention: Patients were treated with 12 months of recombinant human leptin administration to achieve high-normal serum concentrations.

Results: Two patients had both AGL and T1D. The first was diagnosed with T1D at age 8 yr. Beginning at age 11 yr, he developed generalized lipodystrophy, elevated transaminases, and poor glycemic control [hemoglobin A1c (HbA1c) 10.7%] despite markedly increased insulin requirements (3.3–5 U/kg·d). Further evaluation revealed hypoleptinemia and hypertriglyceridemia. At age 15 yr, leptin therapy was initiated, and after 1 yr, his insulin requirements fell to 1 U/kg·d, his glycemic control improved (HbA1c 8.4%), and both his triglycerides and transaminases normalized. The second patient developed concurrent AGL and T1D at age 6 yr. Despite insulin doses of up to 32 U/kg·d, she developed poor glycemic control (HbA1c 10.6%), hypertriglyceridemia (2984 mg/dl), elevated transaminases, and nonalcoholic steatohepatitis. At age 13 yr, leptin therapy was started, and after 1 yr, her glycemic control improved (HbA1c 7.3%) and her insulin requirements decreased (17 U/kg·d). Her triglycerides remained elevated but were improved (441 mg/dl).

Conclusions: Long-term recombinant leptin therapy is effective in treating the insulin resistance of patients with the unusual combination of T1D and AGL.
The surface pair correlation function for stationary Boolean models
Authors: Ballani Felix
Published: October 2007

The random surface measureof a stationary Boolean modelwith grains from the convex ring is considered. A sufficient condition and a necessary condition for the existence of the density of the second-order moment measure ofare given and a representation of this density is derived. As applications, the surface pair correlation functions of a Boolean model with spheres and a Boolean model with randomly oriented right circular cylinders in ℝ3are determined.
Some distributional results for Poisson-Voronoi tessellations
Authors: Baumstark Volker , Last Günter
Published: October 2007

We consider the Voronoi tessellation based on a stationary Poisson process N in ℝd. We provide a complete and explicit description of the Palm distribution describing N as seen from a randomly chosen (typical) point on a k-face of the tessellation. In particular, we compute the joint distribution of the d−k+1 neighbours of the k-face containing the typical point. Using this result as well as a fundamental general relationship between Palm probabilities, we then derive some properties of the typical k-face and its neighbours. Generalizing recent results of Muche (2005), we finally provide the joint distribution of the typical edge (typical 1-face) and its neighbours.
A connection between the volume fractions of the Stienen model and the dead leaves model
Authors: Månsson Marianne
Published: October 2007

The volume fraction of the intact grains of the dead leaves model with spherical grains of equal size is 2−d in d dimensions. This is the volume fraction of the original Stienen model. Here we consider some variants of these models: the dead leaves model with grains of a fixed convex shape and possibly random sizes and random orientations, and a generalisation of the Stienen model with convex grains growing at random speeds. The main result of this paper is that if the radius distribution in the dead leaves model equals the speed distribution in the Stienen model, then the volume fractions of the two models are the same in this case also. Furthermore, we show that for grains of a fixed shape and orientation, centrally symmetric sets give the highest volume fraction, while simplices give the lowest. If the grains are randomly rotated, then the volume fraction achieves its highest value only for spheres.
Multitype shape theorems for first passage percolation models
Authors: Pimentel Leandro P. R.
Published: October 2007

A Euclidean first passage percolation model describing the competing growth between k different types of infection is considered. We focus on the long-time behavior of this multitype growth process and we derive multitype shape results related to its morphology.
Convex duality in constrained mean-variance portfolio optimization
Authors: Labbé Chantal , Heunis Andrew J.
Published: October 2007

We apply conjugate duality to establish the existence of optimal portfolios in an asset-allocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed, finite horizon in a continuous-time, complete market, subject to the constraints that the expected final wealth equal a specified target value and the portfolio of the investor (defined by the dollar amount invested in each stock) take values in a given closed, convex set. The asset prices are modelled by Itô processes, for which the market parameters are random processes adapted to the information filtration available to the investor. We synthesize a dual optimization problem and establish a set of optimality relations, similar to the Euler-Lagrange and transversality relations of calculus of variations, giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution, with zero duality gap. We then solve these relations, to establish the existence of an optimal portfolio.
General convex stochastic orderings and related martingale-type structures
Authors: Vera Francisco , Lynch James
Published: October 2007

Blackwell (1951), in his seminal work on comparison of experiments, ordered two experiments using a dilation ordering: one experiment,Y, is ‘more spread out’ in the sense of dilation than another one,X, if E(c(Y))≥E(c(X)) for all convex functionsc. He showed that this ordering is equivalent to two other orderings, namely (i) atotal time on testordering and (ii) a martingale relationship E(Yʹ |Xʹ)=Xʹ, where (Xʹ,Yʹ) has a joint distribution with the same marginals asXandY. These comparisons are generalized to balayage orderings that are defined in terms of generalized convex functions. These balayage orderings are equivalent to (i) iterated total integral of survival orderings and (ii) martingale-type orderings which we refer to ask-martorderings. These comparisons can arise naturally in model fitting and data confidentiality contexts.
Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary markov chain
Authors: Roquain Etienne , Schbath Sophie
Published: October 2007

We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals.
A new genetic algorithm specifically based on mutation and selection
Authors: Rigal L. , Truffet L.
Published: October 2007

In this paper we propose a new genetic algorithm specifically based on mutation and selection in order to maximize a fitness function. This mutation-selection algorithm behaves as a gradient algorithm which converges to local maxima. In order to obtain convergence to global maxima we propose a new algorithm which is built by randomly perturbing the selection operator of the gradient-like algorithm. The perturbation is controlled by only one parameter: that which allows the selection pressure to be governed. We use the Markov model of the perturbed algorithm to prove its convergence to global maxima. The arguments used in the proofs are based on Freidlin and Wentzell's (1984) theory and large deviation techniques also applied in simulated annealing. Our main results are that (i) when the population size is greater than a critical value, the control of the selection pressure ensures the convergence to the global maxima of the fitness function, and (ii) the convergence also occurs when the population is the smallest possible, i.e. 1.
Stochastic stability of some state-dependent growth-collapse processes
Authors: Robert Christian Y.
Published: October 2007

In this paper we consider a discrete-time process which grows according to a random walk with nonnegative increments between crash times at which it collapses to 0. We assume that the probability of crashing depends on the level of the process. We study the stochastic stability of this growth-collapse process. Special emphasis is given to the case in which the probability of crashing tends to 0 as the level of the process increases. In particular, we show that the process may exhibit long-range dependence and that the crash sizes may have a power law distribution.
Local asymptotics of the cycle maximum of a heavy-tailed random walk
Authors: Denisov Denis , Shneer Vsevolod
Published: October 2007

Let ξ, ξ1, ξ2,… be a sequence of independent and identically distributed random variables, and let Sn=ξ1+⋯+ξn and Mn=maxk≤nSk. Let τ=min{n≥1: Sn≤0}. We assume that ξ has a heavy-tailed distribution and negative, finite mean E(ξ)<0. We find the asymptotics of P{Mτ ∈ (x, x+T]} as x→∞, for a fixed, positive constant T.
On matrix exponential distributions
Authors: He Qi-Ming , Zhang Hanqin
Published: October 2007

In this paper we introduce certain Hankel matrices that can be used to study ME (matrix exponential) distributions, in particular to compute their ME orders. The Hankel matrices for a given ME probability distribution can be constructed if one of the following five types of information about the distribution is available: (i) an ME representation, (ii) its moments, (iii) the derivatives of its distribution function, (iv) its Laplace-Stieltjes transform, or (v) its distribution function. Using the Hankel matrices, a necessary and sufficient condition for a probability distribution to be an ME distribution is found and a method of computing the ME order of the ME distribution developed. Implications for the PH (phase-type) order of PH distributions are examined. The relationship between the ME order, the PH order, and a lower bound on the PH order given by Aldous and Shepp (1987) is discussed in numerical examples.
On spatial thinning-replacement processes based on Voronoi cells
Authors: Borovkov K. A. , Odell D. A.
Published: October 2007

We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is then removed, and a new random point is added to the configuration. The dynamics are simple and intuitive and could be applied to modelling natural phenomena. We prove ergodicity of these processes under wide conditions.
Intersection densities of nonstationary Poisson processes of hypersurfaces
Authors: Hoffmann Lars Michael
Published: October 2007

Intersection densities are introduced for a large class of nonstationary Poisson processes of hypersurfaces and inequalities for them are proved. In doing so, similar results from both Wieacker (1986) and Schneider (2003) are summarized in one theorem and the concept of an associated zonoid of a Poisson process of hypersurfaces is generalized to a nonstationary setting.
The Palm-duality for random subsets of d-dimensional grids
Authors: Thorisson Hermann
Published: October 2007

The Palm version of a stationary random subset of a d-dimensional grid is contructed using the two-step change-of-origin and change-of-measure method. An elementary proof is given of the fact that the Palm version is characterized by point-stationarity (distributional invariance under bijective shifts of the origin from a point of the set to another point of the set).
Explicit laws of large numbers for random nearest-neighbour-type graphs
Authors: Wade Andrew R.
Published: October 2007

Under the unifying umbrella of a general result of Penrose and Yukich (Annals of Applied Probability13 (2003), 277-303) we give laws of large numbers (in the Lp sense) for the total power-weighted length of several nearest-neighbour-type graphs on random point sets in ℝd, d ∈ ℕ. Some of these results are known; some are new. We give limiting constants explicitly, where previously they have been evaluated in less generality or not at all. The graphs we consider include the k-nearest-neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the on-line nearest-neighbour graph.
On the time value of absolute ruin with debit interest
Authors: Cai Jun
Published: October 2007

Assume that the surplus of an insurer follows a compound Poisson surplus process. When the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. Meanwhile, the insurer will repay the debts from her premium income. The negative surplus may return to a positive level. However, when the negative surplus is below a certain critical level, the surplus is no longer able to be positive. Absolute ruin occurs at this moment. In this paper, we study absolute ruin questions by defining an expected discounted penalty function at absolute ruin. The function includes the absolute ruin probability, the Laplace transform of the time to absolute ruin, the deficit at absolute ruin, the surplus just before absolute ruin, and many other quantities related to absolute ruin. First, we derive a system of integro-differential equations satisfied by the function and obtain a defective renewal equation that links the integro-differential equations in the system. Second, we show that when the initial surplus goes to infinity, the absolute ruin probability and the classical ruin probability are asymptotically equal for heavy-tailed claims while the ratio of the absolute ruin probability to the classical ruin probability goes to a positive constant that is less than one for light-tailed claims. Finally, we give explicit expressions for the function for exponential claims.
Ruin probability with certain stationary stable claims generated by conservative flows
Authors: Alparslan Uğur Tuncay , Samorodnitsky Gennady
Published: October 2007

We study the ruin probability where the claim sizes are modeled by a stationary ergodic symmetric α-stable process. We exploit the flow representation of such processes, and we consider the processes generated by conservative flows. We focus on two classes of conservative α-stable processes (one discrete-time and one continuous-time), and give results for the order of magnitude of the ruin probability as the initial capital goes to infinity. We also prove a solidarity property for null-recurrent Markov chains as an auxiliary result, which might be of independent interest.
Approximations for the Gerber-Shiu expected discounted penalty function in the compound poisson risk model
Authors: Pitts Susan M , Politis Konstadinos
Published: October 2007

In the classical risk model with initial capital u, let τ(u) be the time of ruin, X+(u) be the risk reserve just before ruin, and Y+(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function mδ(u) =E[e−δ τ(u)w(X+(u), Y+(u)) 1 (τ(u) < ∞)], where δ ≥ 0 can be interpreted as a force of interest and w(r,s) as a penalty function, meaning that mδ(u) is the expected discounted penalty payable at ruin. This function is known to satisfy a defective renewal equation, but easy explicit formulae for mδ(u) are only available for certain special cases for the claim size distribution. Approximations thus arise by approximating the desired mδ(u) by that associated with one of these special cases. In this paper a functional approach is taken, giving rise to first-order correction terms for the above approximations.
Large deviation properties of constant rate data streams sharing a buffer with long-range dependent traffic in critical loading
Authors: Majewski Kurt
Published: October 2007

We consider a constant rate traffic which shares a buffer with a random cross traffic. A first come first served or priority service discipline is applied at the buffer. After service at the first buffer the constant rate traffic moves to a play-out buffer. Both buffers provide service at constant rate and infinite waiting room. We investigate logarithmic large and moderate deviation asymptotics for the tail probabilities of the steady-state queue length distribution at the play-out buffer for long-range dependent cross traffic in critical loading. We characterize the asymptotic behavior of the cross traffic which leads to a large queue length at the play-out buffer and compare it to the one for renewal cross traffic.
Zero-automatic queues and product form
Authors: Dao-Thi Thu-Ha , Mairesse Jean
Published: October 2007

We introduce and study a new model: zero-automatic queues. Roughly, zero-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable zero-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of zero-automatic queues, we recover the simple M/M/1 queue and Gelenbe's G-queue with positive and negative customers.
Stability of nonlinear stochastic recursions with application to nonlinear AR-GARCH models
Authors: Cline Daren B. H.
Published: October 2007

We characterize the Lyapunov exponent and ergodicity of nonlinear stochastic recursion models, including nonlinear AR-GARCH models, in terms of an easily defined, uniformly ergodic process. Properties of this latter process, known as the collapsed process, also determine the existence of moments for the stochastic recursion when it is stationary. As a result, both the stability of a given model and the existence of its moments may be evaluated with relative ease. The method of proof involves piggybacking a Foster-Lyapunov drift condition on certain characteristic behavior of the collapsed process.
First-crossing and ballot-type results for some nonstationary sequences
Authors: Lefèvre Claude
Published: October 2007

In this paper we consider the problem of first-crossing from above for a partial sums process m+St, t ≥ 1, with the diagonal line when the random variables Xt, t ≥ 1, are independent but satisfying nonstationary laws. Specifically, the distributions of all the Xts belong to a common parametric family of arithmetic distributions, and this family of laws is assumed to be stable by convolution. The key result is that the first-crossing time distribution and the associated ballot-type formula rely on an underlying polynomial structure, called the generalized Abel-Gontcharoff structure. In practice, this property advantageously provides simple and efficient recursions for the numerical evaluation of the probabilities of interest. Several applications are then presented, for constant and variable parameters.
Optimal hitting time and perpetual option in a non-Lévy model: application to real options
Authors: Barrieu P. , Bellamy N.
Published: October 2007

We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After proving the existence of an optimal stopping time for the problem and characterizing it as the hitting time of an optimal boundary, we provide closed-form formulae for the option value, as well as for the Laplace transform of the optimal stopping time. These results are then applied to the analysis of a real option problem when considering the impact of a fundamental and brutal change in the investment project environment. The consequences of this impact, that can seriously modify, positively or negatively, the project's future cash flows and therefore the investment decision, are illustrated by numerical examples.
Inference in Lévy-type stochastic volatility models
Authors: Woerner Jeannette H. C.
Published: October 2007

Based on the concept of multipower variation we establish a class of easily computable and robust estimators for the integrated volatility, especially including the squared integrated volatility, in Lévy-type stochastic volatility models. We derive consistency and feasible distributional results for the estimators. Furthermore, we discuss the applications to time-changed CGMY, normal inverse Gaussian, and hyperbolic models with and without leverage, where the time-changes are based on integrated Cox-Ingersoll-Ross or Ornstein-Uhlenbeck-type processes. We deduce which type of market microstructure does not affect the estimates.
A weighted random walk model, with application to a genetic algorithm
Authors: Dombry C.
Published: October 2007

We consider a weighted random walk model defined as follows. An n-step random walk on the integers with distribution Pn is weighted by giving the path S=(S0,…,Sn) a probability proportional to where the function f is the so-called fitness function. In the case of power-type fitness, we prove the convergence of the renormalized path to a deterministic function with exponential speed. This function is a solution to a variational problem. In the case of the simple symmetric random walk, explicit computations are done. Our result relies on large deviations techniques and Varadhan's integral lemma. We then study an application of this model to mutation-selection dynamics on the integers where a random walk operates the mutation. This dynamics is the infinite-population limit of that of mutation-selection genetic algorithms. We prove that the population grows to ∞ and make explicit its growth speed. This is a toy model for modelling the effect of stronger selection at ∞ for genetic algorithms taking place in a noncompact space.
Markovian paths to extinction
Authors: Jagers Peter , Klebaner Fima C. , Sagitov Serik
Published: October 2007

Subcritical Markov branching processes {Zt} die out sooner or later, say at time T < ∞. We give results for the path to extinction {ZuT, 0 ≤ u ≤ 1} that include its finite dimensional distributions and the asymptotic behaviour of xu−1ZuT, as Z0=x → ∞. The limit reflects an interplay of branching and extreme value theory. Then we consider the population on the verge of extinction, as modelled by ZT-u, u > 0, and show that as Z0= x → ∞ this process converges to a Markov process {Yu}, which we describe completely. Emphasis is on continuous time processes, those in discrete time displaying a more complex behaviour, related to Martin boundary theory.
Random motions at finite velocity in a non-Euclidean space
Authors: Orsingher E. , De Gregorio A.
Published: October 2007

In this paper telegraph processes on geodesic lines of the Poincaré half-space and Poincaré disk are introduced and the behavior of their hyperbolic distances examined. Explicit distributions of the processes are obtained and the related governing equations derived. By means of the processes on geodesic lines, planar random motions (with independent components) in the Poincaré half-space and disk are defined and their hyperbolic random distances studied. The limiting case of one-dimensional and planar motions together with their hyperbolic distances is discussed with the aim of establishing connections with the well-known stochastic representations of hyperbolic Brownian motion. Extensions of motions with finite velocity to the three-dimensional space are also hinted at, in the final section.
Retrieving convex bodies from restricted covariogram functions
Authors: Averkov Gennadiy , Bianchi Gabriele
Published: October 2007

The covariogram gK(x) of a convex body K ⊆ Ed is the function which associates to each x ∈ Ed the volume of the intersection of K with K + x, where Ed denotes the Euclidean d-dimensional space. Matheron (1986) asked whether gK determines K, up to translations and reflections in a point. Positive answers to Matheron's question have been obtained for large classes of planar convex bodies, while for d ≥ 3 there are both positive and negative results. One of the purposes of this paper is to sharpen some of the known results on Matheron's conjecture indicating how much of the covariogram information is needed to get the uniqueness of determination. We indicate some subsets of the support of the covariogram, with arbitrarily small Lebesgue measure, such that the covariogram, restricted to those subsets, identifies certain geometric properties of the body. These results are more precise in the planar case, but some of them, both positive and negative ones, are proved for bodies of any dimension. Moreover some results regard most convex bodies, in the Baire category sense. Another purpose is to extend the class of convex bodies for which Matheron's conjecture is confirmed by including all planar convex bodies possessing two nondegenerate boundary arcs being reflections of each other.
Identities linking volumes of convex hulls
Authors: Cowan Richard
Published: October 2007

Let n points be randomly and independently placed in Rd according to a common probability law. It is known that the expected volume for the convex hull of these points, in the cases where n - d ≥ 2 and even, is related linearly to expected volumes of the convex hulls for j points, j < n. We show that similar identities for these volumes hold almost surely - and in contexts where independence and communality of law do not apply. New geometric and topological identities developed here provide a foundation for this result.
Zero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffs
Authors: Guo Xianping , Hernández-Lerma Onésimo
Published: October 2007

This paper is devoted to the study of two-person zero-sum games for continuous-time jump Markov processes with a discounted payoff criterion. The state and action spaces are all Polish spaces, the transition rates are allowed to be unbounded, and the payoff rates may have neither upper nor lower bounds. We give conditions on the game's primitive data under which the existence of a solution to the Shapley equation is ensured. Then, from the Shapley equation, we obtain the existence of the value of the game and of a pair of optimal stationary strategies using the extended infinitesimal operator associated with the transition function of a possibly nonhomogeneous continuous-time jump Markov process. We also provide a recursive way of computing (or at least approximating) the value of the game. Moreover, we present a ‘martingale characterization’ of a pair of optimal stationary strategies. Finally, we apply our results to a controlled birth and death system and a Schlögl first model, and then we use controlled Potlach processes to illustrate our conditions.
Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs
Authors: Paulsen Jostein
Published: October 2007

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.
On the distribution of the limit proportion for a two-color, randomly reinforced urn with equal reinforcement distributions
Authors: Aletti Giacomo , May Caterina , Secchi Piercesare
Published: October 2007

We consider a two-color, randomly reinforced urn with equal reinforcement distributions and we characterize the distribution of the urn's limit proportion as the unique continuous solution of a functional equation involving unknown probability distributions on [0, 1].
The Hausdorff dimension of a class of random self-similar fractal trees
Authors: Croydon D. A.
Published: October 2007

In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical properties of an underlying metric space or the scaling factors being bounded uniformly away from 0. However, using a percolative argument, and taking advantage of the tree-like structure of the sets considered here, it is shown that conditions such as these are not necessary. The scaling factors of the recursively defined structures in consideration form what is known as a multiplicative cascade, and results about the height of this random object are also obtained.
CLT-related large deviation bounds based on Stein's method
Authors: Raič Martin
Published: October 2007

Large deviation estimates are derived for sums of random variables with certain dependence structures, including finite population statistics and random graphs. The argument is based on Stein's method, but with a novel modification of Stein's equation inspired by the Cramér transform.
Corrected random walk approximations to free boundary problems in optimal stopping
Authors: Lai Tze Leung , Yao Yi-Ching , Aitsahlia Farid
Published: October 2007

Corrected random walk approximations to continuous-time optimal stopping boundaries for Brownian motion, first introduced by Chernoff and Petkau, have provided powerful computational tools in option pricing and sequential analysis. This paper develops the theory of these second-order approximations and describes some new applications.
Asymptotics for local maximal stack scores with general loop penalty function
Authors: Hansen Niels Richard
Published: October 2007

A stack is a structural unit in an RNA structure that is formed by pairs of hydrogen bonded nucleotides. Paired nucleotides are scored according to their ability to hydrogen bond. We consider stack/hairpin-loop structures for a sequence of independent and identically distributed random variables with values in a finite alphabet, and we show how to obtain an asymptotic Poisson distribution of the number of stack/hairpin-loop structures with a score exceeding a high threshold, given that we count in a proper, declumped way. From this result we obtain an asymptotic Gumbel distribution of the maximal stack score. We also provide examples focusing on the computation of constants that enter in the asymptotic distributions. Finally, we discuss the close relation to existing results for local alignment.
r-scan statistics of a Poisson process with events transformed by duplications, deletions, and displacements
Authors: Chen Chingfer , Karlin Samuel
Published: October 2007

A stochastic model of a dynamic marker array in which markers could disappear, duplicate, and move relative to its original position is constructed to reflect on the nature of long DNA sequences. The sequence changes of deletions, duplications, and displacements follow the stochastic rules: (i) the original distribution of the marker array {…,X−2,X−1,X0,X1,X2, …} is a Poisson process on the real line; (ii) each marker is replicatedltimes; replication or loss of marker points occur independently; (iii) each replicated point is independently and randomly displaced by an amountYrelative to its original position, with theYdisplacements sampled from a continuous densityg(y). Limiting distributions for the maximal and minimal statistics of ther-scan lengths (collection of distances betweenr+ 1 successive markers) for thel-shift model are derived with the aid of the Chen-Stein method and properties of Poisson processes.
Asymptotic expansions on moments of the first ladder height in Markov random walks with small drift
Authors: Fuh Cheng-Der
Published: October 2007

Let {(Xn, Sn), n ≥ 0} be a Markov random walk in which Xn takes values in a general state space and Sn takes values on the real line R. In this paper we present some results that are useful in the study of asymptotic approximations of boundary crossing problems for Markov random walks. The main results are asymptotic expansions on moments of the first ladder height in Markov random walks with small positive drift. In order to establish the asymptotic expansions we study a uniform Markov renewal theorem, which relates to the rate of convergence for the distribution of overshoot, and present an analysis of the covariance between the first passage time and the overshoot.
Rendezvous Search with Revealed Information: Applications to the Line
Authors: Alpern Steve
Published: October 2007

The symmetric rendezvous problem on a network Q asks how two players, forced to use the same mixed strategy, can minimize their expected meeting time, starting from a known initial distribution on the nodes of Q. This minimum is called the (symmetric) ‘rendezvous value’ of Q. Traditionally, the players are assumed to receive no information while playing the game. We consider the effect on rendezvous times of giving the players some information about past actions and chance moves, enabling each of them to apply Bayesian updates to improve his knowledge of the other's whereabouts. This technique can be used to give lower bounds on the rendezvous times of the original game (without any revealed information). We consider the case in which they are placed a known distance apart on the line graph Q (known as ‘symmetric rendezvous on the line’). Our approach is to concentrate on a general analysis of the effect of revelations, rather than compute the best bounds possible with our technique.
Coupling of Two SIR Epidemic Models with Variable Susceptibilities and Infectivities
Authors: Neal Peter
Published: October 2007

The variable generalised stochastic epidemic model, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic model which exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.
Thou Shalt not Diversify: Why ‘Two Of Every Sort’?
Authors: Ibragimov Rustam
Published: October 2007

This paper presents a study of the intertemporal propagation of distributional properties of phenotypes in general polygenic multisex inheritance models with sex- and time-dependent heritabilities. It further analyzes the implications of these models under heavy-tailedness of traits' initial distributions. Our results suggest the optimality of a flexible asexual/binary mating system. Switching between asexual and binary inheritance mechanisms allows the population effectively to achieve a fast suppression of negative traits and a fast dispersion of positive traits, regardless of the distributional properties of the phenotypes in the initial period.
Large Deviations Principle for Occupancy Problems with Colored Balls
Authors: Dupuis Paul , Nuzman Carl , Whiting Phil
Published: October 2007

A large deviations principle (LDP), demonstrated for occupancy problems with indistinguishable balls, is generalized to the case in which balls are distinguished by a finite number of colors. The colors of the balls are chosen independently from the occupancy process itself. There arerballs thrown intonurns with the probability of a ball entering a given urn being 1/n(i.e. Maxwell-Boltzmann statistics). The LDP applies with the scale parameter,n, tending to infinity andrincreasing proportionally. The LDP holds under mild restrictions, the key one being that the coloring process by itself satisfies an LDP. This includes the important special cases of deterministic coloring patterns and colors chosen with fixed probabilities independently for each ball.
Comparison Results for Branching Processes in Random Environments
Authors: Pellerey Franco
Published: October 2007

In this note we consider branching processes whose behavior depends on a dynamic random environment, in the sense that we assume that the offspring distributions of individuals are parametrized, over time, by the realizations of a process describing the environmental evolution. We study how the variability in time of the environment modifies the variability of total population by considering two branching processes of this kind (but subjected to different environments). We also provide conditions on the random environments in order to stochastically compare their marginal distributions in the increasing convex sense. Weaker conditions are also provided for comparisons at every fixed time of the expected values of the two populations.
Arbitrary Threshold Widths for Monotone, Symmetric Properties
Authors: Rossignol Raphaël
Published: October 2007

We show that there exist symmetric properties in the discreten-cube whose threshold widths range asymptotically between 1/√nand 1/logn. These properties are built using a combination of failure sets arising in reliability theory. This combination of sets is simply called a product. Some general results on the threshold width of the product of two setsAandBin terms of the threshold locations and widths ofAandBare provided.
On Threshold Strategies and the Smooth-Fit Principle for Optimal Stopping Problems
Authors: Villeneuve Stéphane
Published: October 2007

In this paper we investigate sufficient conditions that ensure the optimality of threshold strategies for optimal stopping problems with finite or perpetual maturities. Our result is based on a local-time argument that enables us to give an alternative proof of the smooth-fit principle. Moreover, we present a class of optimal stopping problems for which the propagation of convexity fails.
Optimal Strategy for the Vardi Casino with Interest Payments
Authors: Grigorescu Ilie , Chen Robert , Shepp Larry
Published: October 2007

A gambler starts with fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c < 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.
Optimal Control of a Large Dam
Authors: Abramov Vyacheslav M.
Published: October 2007

A large dam model is the object of study of this paper. The parameters Llower and Lupper define its lower and upper levels,
L = Lupper - Llower is large, and if the current level of water is between these bounds, the dam is assumed to be in a normal state. Passage across one or other of the levels leads to damage. Let J1 and J2 denote the damage costs of crossing the lower and, respectively, the upper levels. It is assumed that the input stream of water is described by a Poisson process, while the output stream is state dependent. Let Lt denote the dam level at time t, and let p1 = limt→∞P{Lt = Llower} and p2 = limt→∞P{Lt > Lupper} exist. The long-run average cost,
J = p1J1 + p2J2, is a performance measure. The aim of the paper is to choose the parameter controlling the output stream so as to minimize J.
Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems
Authors: Bompadre Agustín , Dror Moshe , Orlin James B.
Published: October 2007

We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.
A Remark on the Uniqueness of Weighted Markov Branching Processes
Authors: Chen Anyue , Pollett Phil , Li Junping , Zhang Hanjun
Published: October 2007

We present an elegant uniqueness criterion for the weighted Markov branching process in the potentially explosive case.
Tail Asymptotics for Monotone-Separable Networks
Authors: Lelarge Marc
Published: October 2007

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.
A Stochastic Ordering Property for Leaky Bucket Regulated Flows in Packet Networks
Authors: Guillemin Fabrice M. , Mazumdar Ravi R. , Rosenberg Catherine P. , Ying Yu
Published: October 2007

We show in this paper that if a stationary traffic source is regulated by a leaky bucket with leak rate ρ and bucket size σ, then the amount of information generated in successive time intervals is dominated, in the increasing convex ordering sense, by that of a Poisson arrival process with rate ρ/σ, with each arrival bringing an amount of information equal to σ. By exploiting this property, we then show that the mean value in the stationary regime of the content of a buffer drained at constant rate and fed with the superposition of regulated flows is less than the mean value of the same buffer fed with an adequate Poisson process, whose characteristics depend upon the regulated input flows.
A Diffusion Approximation for Markov Renewal Processes
Authors: Clark Steven P. , Kiessler Peter C.
Published: October 2007

For a Markov renewal process where the time parameter is discrete, we present a novel method for calculating the asymptotic variance. Our approach is based on the key renewal theorem and is applicable even when the state space of the Markov chain is countably infinite.
Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion
Authors: Sly Allan
Published: October 2007

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.
Distribution of the Present Value of Dividend Payments in a Lévy Risk Model
Authors: Renaud Jean-François , Zhou Xiaowen
Published: October 2007

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.
A Stability Property of Stochastic Vibration
Authors: Elshamy M.
Published: October 2007

Let u(t,x) be the displacement at time t of a point x on a string; the time variable t varies in the interval I≔[0,T] and the space variable x varies in the interval J≔[0,L], where T and L are fixed positive constants. The displacement u(t,x) is the solution to a stochastic wave equation. Two forms of random excitations are considered, a white noise in the initial condition and a nonlinear random forcing which involves the formal derivative of a Brownian sheet. In this article, we consider the continuity properties of solutions to this equation. Smoothness characteristics of these random fields, in terms of Hölder continuity, are also investigated.