bluuebunny/crossref_metadata_2025 huggingface dataset:
Mahzar-namas in the Mughal and British Empires: The Uses of an Indo-Islamic Legal Form
Authors: Chatterjee Nandini
Published: March 2016

This paper looks at a Persian-language documentary form called the mahzar-nama that was widely used in India between the seventeenth and nineteenth centuries to narrate, represent, and record antecedents, entitlements, and injuries with a view to securing legal rights and redressing legal wrongs. Mahzars were a known documentary form in Islamic law and used by qazis (Islamic judges) in many other parts of the world, but in India they took a number of distinctive forms. The specific form of Indian mahzar-namas that I focus on here was, broadly speaking, a legal document of testimony, narrated in the first person, in a form standardized by predominantly non-Muslim scribes, endorsed in writing by the author's fellow community members and/or professional or social contacts, and notarized by a qazi's seal. This specific legal form was part of a much broader genre of declarative texts that were also known as mahzars in India. I examine the legal mahzar-namas together with the other kinds of mahzars, and situate them in relation to Indo-Islamic jurisprudential texts and Persian-language formularies. What emerges is a distinctive Indo-Islamic legal culture in contact with the wider Islamic and Persianate worlds of jurisprudence and documentary culture, but responsive to the unique socio-political formations of early modern India. I also reflect on the meanings of law, including Islamic law, for South Asians and trace the evolution of that understanding across the historical transition to colonialism.
The Politics of Gift Exchange in Early Qajar Iran, 1785–1834
Authors: Ashraf Assef
Published: March 2016

This article uses gift-giving practices in early nineteenth-century Iran as a window onto statecraft, governance, and center-periphery relations in the early Qajar state (1785–1925). It first demonstrates that gifts have a long history in the administrative and political history of Iran, the Persianate world, and broader Eurasia, before highlighting specific features found in Iran. The article argues that the pīshkish, a tributary gift-giving ceremony, constituted a central role in the political culture and economy of Qajar Iran, and was part of the process of presenting Qajar rule as a continuation of previous Iranian royal dynasties. Nevertheless, pīshkish ceremonies also illustrated the challenges Qajar rulers faced in exerting power in the provinces and winning the loyalty of provincial elites. Qajar statesmen viewed gifts and bribes, at least at a discursive level, in different terms, with the former clearly understood as an acceptable practice. Gifts and honors, like the khil‘at, presented to society were part of Qajar rulers' strategy of presenting themselves as just and legitimate. Finally, the article considers the use of gifts to influence diplomacy and ease relations between Iranians and foreign envoys, as well as the ways in which an inadequate gift could cause offense.
SOME PROUD WORDS FROM THE INCOMING EDITOR-IN-CHIEF
Authors: Ribeiro Rafael V.
Published: March 2016

Firstly, I would like to say that it is a great honour to take over the position of Editor-in-chief of Experimental Agriculture, one of the most important journals devoted to publishing original and high quality papers addressing the many facets of agricultural sciences in subtropical and tropical areas. Tradition! I would say that this single word has an enormous meaning for me. I am proud in serving Experimental Agriculture, a journal published by the Cambridge University Press since 1933. Originally titled The Empire Journal of Experimental Agriculture (1933-1964), the publication's mission was ambitious “every new fruit of discovery and invention in the agricultural field”, publishing critical information for improving agricultural systems. So pertinent was the Journal's remit that it was recognised in an article published in Nature in May 27th, 1933. Currently, Experimental Agriculture has an Impact Factor of 1.079 (ISI Thomson Reuters) and stands as a Q1 journal in ‘Agronomy and Crop Science’ (SCImago Journal and Country Rank). In 2015, we received submissions from the five continents, with the majority coming from Asia and Africa. Thank you for considering Experimental Agriculture as a potential journal to publish your paper!
Contrasting patterns of preservation in a Jamaican cave
Authors: DONOVAN STEPHEN K.
Published: March 2016

Red Hills Road Cave, Jamaica is a remnant of a karstic feature quarried away during road building. It is the most important site for Late Pleistocene terrestrial palaeontology on the island. The site isc. 30 ka old. Many taxa were washed in during hurricanes and tropical storms, either as dead carcasses or live organisms that drowned as the cave filled with water. The invertebrate fauna includes snails and arthropods; none are obligate cave dwellers. The 62 species of land snails are the most diverse of any Jamaican cave; operculate taxa may be preserved with the operculumin situ. Arthropods include the only fossil millipedes, isopods and insects (fly puparia, beetle elytra) in the Jamaican fossil record, in addition to land crabs. Millipedes and isopods are well preserved because of a diagenetically early coating of calcite cement. The exoskeletons of these groups contain a small, but significant, calcite component not found in insects, spiders and scorpions. The vertebrate fauna remains understudied, but include: a rodent and three species of bat; a flightless ibis and various other birds; and reptile and amphibian remains. In contrast to the arthropods, the vertebrates are invariably disarticulated apart from rare crania, jawbones retaining teeth and bones that are fused in life. A dead millipede could be coated in calcite when floating in the cave immediately after death; a dead vertebrate carcass would have to rot to expose its bones after the cave dried out and would, most likely, disarticulate before or during the next inundation.
IMMORTAL ACHILLES
Authors: Burton Diana
Published: March 2016

During the early archaic period, there was considerable interest in the heroic past and the acts of mythical ancestors, especially as embodied in epic. In particular, there are a number of archaic myths dealing with attempts to evade death and to gain immortality, mostly unsuccessful. All Greek heroes are descended from gods: having at least one god (or goddess) somewhere in the family tree is a prerequisite for achieving anything worthy of note. And in a few heroes, this sliver of divinity may be turned into full-blown immortality. It is a recurring theme in Greek myth, therefore, that there is a narrow window of possibility for a hero to escape his mortal status and not have to die. Behind such myths lies the fiction that, in a past age, immortality had been attainable; the heroes of the past might not have been immortalized often, but the chance had been there. This was contrasted with the present duller age, in which immortality was out of reach.
‘CHRIST, OUR LEONIDAS’: DRACONTIUS’ RECEPTION OF THE BATTLE OF THERMOPYLAE
Authors: Murray Jeffrey
Published: March 2016

One of the final images of Zack Snyder's 2006 box-office-hit film, 300, is of Leonidas, the Spartan king, lying dead on the ground surrounded by his fellow Spartans, having been shot to death by a vast number of Persian arrows. The camera pans over the bruised and bloodied Spartan dead until it finally comes to rest on Leonidas himself, his arms spread out in a gesture that curiously imitates the iconography of the crucifixion of Christ. Whether done explicitly or not, this is not the only time in its reception history that the story of Leonidas’ last stand has been linked with Christ's sacrifice on the cross, or with Christianity more generally. In this article, I will explore some aspects of the story of the battle of Thermopylae's reception by the Carthaginian Christian poet Dracontius.
Art and Archaeology
Authors: Spivey Nigel
Published: March 2016

In 1830 a hoard of Roman silver weighing some 25 kilograms was recovered from farmland near Berthouville, between Rouen and Caen. The silver was mostly worked into drinking vessels and associated items such as jugs, ladles, and bowls. Two statuettes of the god Mercury confirmed this as a votive deposit, as indicated by various dedications from Romano-Gallic pilgrims, notably on nine pieces left by Quintus Domitius Tutus (‘Mr Safe’) in the mid-first century ad. Restored by conservation experts at the Getty Museum, the cache – along with several other treasures from Gaul – has served as witness to ‘Roman luxury’ in an exhibition on tour in the USA. The exhibition's catalogue is a volume that earns its place in any classical library. The Berthouville Silver Treasure and Roman Luxury may not add very much to our understanding of luxuria in Roman discourse: it is left unclear what happens when a ‘luxury object’ is put out of circulation, or at least transferred into the enclosed economy of a sanctuary; and if Mercury was a deity of fortune favoured particularly by freed slaves, perhaps a set of silver spoons was not such an ‘elite’ attribute as supposed? Beyond such factors of value, however, the figurative elaboration on display is striking. At the centre of a libation bowl we find the Lydian queen Omphale in a drunken slumber, exposing her derrière – as if to say ‘Beware how you imbibe’. One wine pitcher shows Achilles leaping aboard his chariot, with the body of Hector trussed in tow; turn the jug round, and there is Achilles again, now himself stricken in battle. On another pitcher, Achilles is among Greeks mourning the death of Patroclus; and there is Hector's corpse in a pair of scales, as the price of his ransom is assessed. We would be impressed to find such ‘sophisticated’ iconography upon objects in use at some stately villa at Rome or around the Bay of Naples. What does its appearance in the moist pastures of Normandy signify – at least for our preconceptions of ‘provincial taste’?
Central Limit Theorems for Law-Invariant Coherent Risk Measures
Authors: Belomestny Denis , Krätschmer Volker
Published: March 2016

In this paper we study the asymptotic properties of the canonical plugin estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent and identically distributed data, and then extend it to the case of weakly dependent data. Finally, a number of illustrating examples is presented.
Phase-Type Distributions and Optimal Stopping for Autoregressive Processes
Authors: Christensen Sören
Published: March 2016

Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications, the overshoot and the threshold time are of special interest. When the upward innovations are in the class of phase-type distributions, we determine the joint distribution of these two quantities and apply this result to problems of optimal stopping. Using a principle of continuous fit, this leads to explicit solutions.
A Recurrent Solution of PH/M/c/N-Like and PH/M/c-Like Queues
Authors: Brandwajn Alexandre , Begin Thomas
Published: March 2016

We propose an efficient semi-numerical approach to compute the steady-state probability distribution for the number of requests at arbitrary and at arrival time instants in PH/M/c-like systems with homogeneous servers in which the inter-arrival time distribution is represented by an acyclic set of memoryless phases. Our method is based on conditional probabilities and results in a simple computationally stable recurrence. It avoids the explicit manipulation of potentially large matrices and involves no iteration. Owing to the use of conditional probabilities, it delays the onset of numerical issues related to floating-point underflow as the number of servers and/or phases increases. For generalized Coxian distributions, the computational complexity of the proposed approach grows linearly with the number of phases in the distribution.
On a Class of Distributions Stable Under Random Summation
Authors: Klebanov L. B. , Kakosyan A. V. , Rachev S. T. , Temnov G.
Published: March 2016

We study a family of distributions that satisfy the stability-under-addition property, provided that the number ν of random variables in a sum is also a random variable. We call the corresponding property ν-stability and investigate the situation when the semigroup generated by the generating function of ν is commutative. Using results from the theory of iterations of analytic functions, we describe ν-stable distributions generated by summations with rational generating functions. A new case in this class of distributions arises when generating functions are linked with Chebyshev polynomials. The analogue of normal distribution corresponds to the hyperbolic secant distribution.
Backward Coalescence Times for Perfect Simulation of Chains with Infinite Memory
Authors: De Santis Emilio , Piccioni Mauro
Published: March 2016

This paper is devoted to the perfect simulation of a stationary process with an at most countable state space. The process is specified through a kernel, prescribing the probability of the next state conditional to the whole past history. We follow the seminal work of Comets, Fernández and Ferrari (2002), who gave sufficient conditions for the construction of a perfect simulation algorithm. We define backward coalescence times for these kind of processes, which allow us to construct perfect simulation algorithms under weaker conditions than in Comets, Fernández and Ferrari (2002). We discuss how to construct backward coalescence times (i) by means of information depths, taking into account some a priori knowledge about the histories that occur; and (ii) by identifying suitable coalescing events.
A Symmetry Property for a Class of Random Walks in Stationary Random Environments on Z
Authors: Derrien Jean-Marc , Plantevin Frédérique
Published: March 2016

A correspondence formula between the laws of dual Markov chains on Z with two transition jumps is established. This formula contributes to the study of random walks in stationary random environments. Counterexamples with more than two jumps are exhibited.
On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes
Authors: Borovkov K. , Last G.
Published: March 2016

LetX= {Xt:t≥ 0} be a stationary piecewise continuousRd-valued process that moves between jumps along the integral curves of a given continuous vector field, and letS⊂Rdbe a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings ofSbyXto the distribution ofX0. Our result is illustrated by examples relating to queueing networks and stress release network models.
Hurst Index of Functions of Long-Range-Dependent Markov Chains
Authors: Oğuz Barlas , Anantharam Venkat
Published: March 2016

A positive recurrent, aperiodic Markov chain is said to be long-range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long-range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queueing networks, source compression, and finance.
On Tail Bounds for Random Recursive Trees
Authors: Munsonius Götz Olaf
Published: March 2016

We consider a multivariate distributional recursion of sum type, as arises in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the Laplace transform. The problem is traced back to the corresponding problem for binary search trees by stochastic domination. The result obtained is applied to the internal path length and Wiener index of randomb-ary recursive trees with weighted edges and random linear recursive trees. Finally, lower tail bounds for the Wiener index of these trees are given.
Sample Path Optimal Policies for Serial Lines with Flexible Workers
Authors: Pandelis Dimitrios G. , Van Oyen Mark P.
Published: March 2016

We study the dynamic assignment of cross-trained workers in serial production lines characterized by stochastic process times and inventory buffers between stations. Throughput maximization is the objective. Each worker is trained for a subset of tasks, where emphasis is placed on systems with each worker trained for a zone of stations with stations near the zone boundaries being served (shared) by one or more other workers as well. Using sample path comparisons, we identify structural properties of optimal worker allocation policies. We identify when (i) a worker can prioritize the job in the most downstream station (last-buffer-first-served), and (ii) only the downstream (as opposed to upstream) server should serve a single task.
Means and Variances in Stochastic Multistage Cancer Models
Authors: Sudbury Aidan
Published: March 2016

A widely used model of carcinogenesis assumes that cells must go through a process of acquiring several mutations before they become cancerous. This implies that at any time there will be several populations of cells at different stages of mutation. In this paper we give exact expressions for the expectations and variances of the number of cells in each stage of such a stochastic multistage cancer model.
Coalescence in Critical and Subcritical Galton-Watson Branching Processes
Authors: Athreya K. B.
Published: March 2016

In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation X

n
a pairwise coalescence time. Similarly, let Y

n

denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of X

n
and Y

n
, and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.
The Probability of the Alabama Paradox
Authors: Janson Svante , Linusson Svante
Published: March 2016

Hamilton's method is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In the USA it has been abandoned due to some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries. In this paper we give, under certain assumptions, a closed formula for the asymptotic probability, as the number of seats tends to infinity, that the Alabama paradox occurs given the vector p
1,…, p

m

of relative sizes of the states. From the formula we deduce a number of consequences. For example, the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1 / e and on average approximately 0.123.
Almost Giant Clusters for Percolation on Large Trees with Logarithmic Heights
Authors: Bertoin Jean
Published: March 2016

This paper is based on works presented at the 2012 Applied Probability Trust Lecture in Sheffield; its main purpose is to survey the recent asymptotic results of Bertoin (2012a) and Bertoin and Uribe Bravo (2012b) about Bernoulli bond percolation on certain large random trees with logarithmic height. We also provide a general criterion for the existence of giant percolation clusters in large trees, which answers a question raised by David Croydon.
Factorization Identities for Reflected Processes, with Applications
Authors: Fralix Brian H. , van Leeuwaarden Johan S. H. , Boxma Onno J.
Published: March 2016

We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy processes starting at an arbitrary initial state. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth‒death processes and diffusion processes.
On Largest Offspring in a Critical Branching Process with Finite Variance
Authors: Bertoin Jean
Published: March 2016

Continuing the work in Bertoin (2011) we study the distribution of the maximal number X
*

k
of offspring amongst all individuals in a critical Galton‒Watson process started with k ancestors, treating the case when the reproduction law has a regularly varying tail F̅ with index −α for α > 2 (and, hence, finite variance). We show that X
*

k
suitably normalized converges in distribution to a Fréchet law with shape parameter α/2; this contrasts sharply with the case 1< α<2 when the variance is infinite. More generally, we obtain a weak limit theorem for the offspring sequence ranked in decreasing order, in terms of atoms of a certain doubly stochastic Poisson measure.
On Stochastic Predictions of Failure Processes Under Population Heterogeneity
Authors: Cha Ji Hwan
Published: March 2016

In reliability a number of failure processes for repairable items are described by point processes, depending on the types of repairs being performed on failures of items. In this paper we describe the failure processes of repairable items from heterogeneous populations and study the stochastic predictions of future processes which utilize the failure/repair history. Two types of repair processes, perfect and minimal repair processes, will be considered. The results will be derived under a general stochastic formulation/setting. Applications of the obtained results to many different areas will be discussed and, specifically, some reliability applications will be illustrated in detail.
On Multiply Monotone Distributions, Continuous or Discrete, with Applications
Authors: Lefèvre Claude , Loisel Stéphane
Published: March 2016

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer ordert. A characterization is presented as a mixture of a minimum oftindependent uniform distributions. Then, a comparison oft-monotone distributions is made using thes-convex stochastic orders. A link is also pointed out with an alternative approach to monotonicity based on a stationary-excess operator. Finally, the monotonicity property is exploited to reinforce the classical Markov and Lyapunov inequalities. The results are illustrated by several applications to insurance.
Fractional Discrete Processes: Compound and Mixed Poisson Representations
Authors: Beghin Luisa , Macci Claudio
Published: March 2016

We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Pólya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters.
On the Location of the Maximum of a Continuous Stochastic Process
Authors: Pimentel Leandro P. R.
Published: March 2016

In this short article we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the derivative of the expectation of the maximum of a linear perturbation of the underlying process. As an application, we will consider a Brownian motion with variable drift. The ideas behind the method of proof will also be useful to study the location of the maximum, over the real line, of a two-sided Brownian motion minus a parabola and of a stationary process minus a parabola.
Species Dynamics in the Two-Parameter Poisson-Dirichlet Diffusion Model
Authors: Ruggiero Matteo
Published: March 2016

The recently introduced two-parameter infinitely-many-neutral-alleles model extends the celebrated one-parameter version (which is related to Kingman's distribution) to diffusive two-parameter Poisson-Dirichlet frequencies. In this paper we investigate the dynamics driving the species heterogeneity underlying the two-parameter model. First we show that a suitable normalization of the number of species is driven by a critical continuous-state branching process with immigration. Secondly, we provide a finite-dimensional construction of the two-parameter model, obtained by means of a sequence of Feller diffusions of Wright-Fisher flavor which feature finitely many types and inhomogeneous mutation rates. Both results provide insight into the mathematical properties and biological interpretation of the two-parameter model, showing that it is structurally different from the one-parameter case in that the frequency dynamics are driven by state-dependent rather than constant quantities.
Stopping Probabilities for Patterns in Markov Chains
Authors: Gava Renato Jacob , Salotti Danilo
Published: March 2016

Consider a sequence of Markov-dependent trials where each trial produces a letter of a finite alphabet. Given a collection of patterns, we look at this sequence until one of these patterns appears as a run. We show how the method of gambling teams can be employed to compute the probability that a given pattern is the first pattern to occur.
On a ‘Replicating Character String’ Model
Authors: Bradley Richard C.
Published: March 2016

In Chaudhuri and Dasgupta's 2006 paper a certain stochastic model for ‘replicating character strings’ (such as in DNA sequences) was studied. In their model, a random ‘input’ sequence was subjected to random mutations, insertions, and deletions, resulting in a random ‘output’ sequence. In this paper their model will be set up in a slightly different way, in an effort to facilitate further development of the theory for their model. In their 2006 paper, Chaudhuri and Dasgupta showed that, under certain conditions, strict stationarity of the ‘input’ sequence would be preserved by the ‘output’ sequence, and they proved a similar ‘preservation’ result for the property of strong mixing with exponential mixing rate. In our setup, we will in spirit slightly extend their ‘preservation of stationarity’ result, and also prove a ‘preservation’ result for the property of absolute regularity with summable mixing rate.
A Stochastic Model for Virus Growth in a Cell Population
Authors: Björnberg J. E. , Britton T. , Broman E. I. , Natan E.
Published: March 2016

In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.
The Explicit Laplace Transform for the Wishart Process
Authors: Gnoatto Alessandro , Grasselli Martino
Published: March 2016

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral, which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation-of-constants method, the linearization of the matrix Riccati ordinary differential equation, and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.
Minimal Clade Size in the Bolthausen-Sznitman Coalescent
Authors: Freund Fabian , Siri-Jégousse Arno
Published: March 2016

In this article we show the asymptotics of distribution and moments of the sizeXnof the minimal clade of a randomly chosen individual in a Bolthausen-Sznitmann-coalescent forn→ ∞. The Bolthausen-Sznitmann-coalescent is a Markov process taking states in the set of partitions of {1, …,n}, where 1, …,nare referred to as individuals. The minimal clade of an individual is the equivalence class the individual is in at the time of the first coalescence event this individual participates in. We also provide exact formulae for the distribution ofXn. The main tool used is the connection of the Bolthausen-Sznitmann-coalescent with random recursive trees introduced by Goldschmidt and Martin (2005). With it, we show thatXn- 1 is distributed as the size of a uniformly chosen table in a standard Chinese restaurant process withn- 1 customers.
Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory
Authors: Biard Romain , Saussereau Bruno
Published: March 2016

We study a renewal risk model in which the surplus process of the insurance company is modelled by a compound fractional Poisson process. We establish the long-range dependence property of this nonstationary process. Some results for ruin probabilities are presented under various assumptions on the distribution of the claim sizes.
Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity
Authors: Martínez Servet , San Martín Jaime , Villemonais Denis
Published: March 2016

We study the long-time behaviour of a Markov process evolving inNand conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a uniquequasistationary distribution(in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported inN*if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.
Invariant Bipartite Random Graphs on Rd
Authors: Lopes Fabio
Published: March 2016

Suppose that red and blue points occur inRdaccording to two simple point processes with finite intensities λRand λB, respectively. Furthermore, let ν and μ be two probability distributions on the strictly positive integers with means ν̅ and μ̅, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law ν (μ). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law ν or μ depending on its color. For a large class of point processes, we show that such translation-invariant schemes matching almost surely all stubs are possible if and only if λRν̅ = λBμ̅, including the case when ν̅ = μ̅ = ∞ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme, we give sufficient conditions on ν and μ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and Häggström.
Asymptotic Behaviour of the Time-Fractional Telegraph Equation
Authors: Vergara Vicente
Published: March 2016

We obtain the long-time behaviour to the variance of the distribution process associated with the solution of the telegraph equation. To this end, we use a version of the Karamata-Feller Tauberian theorem.
Type Transition of Simple Random Walks on Randomly Directed Regular Lattices
Authors: Campanino Massimo , Petritis Dimitri
Published: March 2016

Simple random walks on a partially directed version ofZ2are considered. More precisely, vertical edges between neighbouring vertices ofZ2can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function; the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.
The Hawkes Process with Different Exciting Functions and its Asymptotic Behavior
Authors: Fierro Raúl , Leiva Víctor , Møller Jesper
Published: March 2016

The standard Hawkes process is constructed from a homogeneous Poisson process and uses the same exciting function for different generations of offspring. We propose an extension of this process by considering different exciting functions. This consideration may be important in a number of fields; e.g. in seismology, where main shocks produce aftershocks with possibly different intensities. The main results are devoted to the asymptotic behavior of this extension of the Hawkes process. Indeed, a law of large numbers and a central limit theorem are stated. These results allow us to analyze the asymptotic behavior of the process when unpredictable marks are considered.
Extremes of Homogeneous Gaussian Random Fields
Authors: Dębicki Krzysztof , Hashorva Enkelejd , Soja-Kukieła Natalia
Published: March 2016

Let {X(s, t): s, t ≥ 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r(s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - |s|α1
- |t|α2
+ o(|s|α1
+ |t|α2
), s, t → 0, with α1, α2 ∈ (0, 2], and r(s, t) < 1 for (s, t) ≠ (0, 0). In this contribution we derive an asymptotic expansion (as u → ∞) of P(sup(sn
1(u),tn
2(u)) ∈[0,x]∙[0,y]
X(s, t) ≤ u), where n
1(u)n
2(u) =
u
2/α1+2/α2
Ψ(u), which holds uniformly for (x, y) ∈ [A, B]2 with A, B two positive constants and Ψ the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X(s, t).
Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings
Authors: Kosiński K. M. , Mandjes M.
Published: March 2016

Let
W
= {
W

n
: n ∈ N} be a sequence of random vectors in R

d
, d ≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of
W
, that is, for any vector
q
> 0 in R

d
, we find that logP(there exists n ∈ N:
W

n

u

q
) as u → ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every
q
≥ 0, and some scalings {a

n
}, {v

n
}, (1 / v

n
)logP(
W

n
/
a

n
≥ u

q
) has a, continuous in
q
, limit J

W

(
q
). We allow the scalings {a

n
} and {v

n
} to be regularly varying with a positive index. This approach is general enough to incorporate sequences
W
, such that the probability law of
W

n
/ a

n
satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.
Extreme Dispersions of Semicoherent and Mixed System Lifetimes
Authors: Miziuła Patryk , Rychlik Tomasz
Published: March 2016

We consider semicoherent and mixed systems with exchangeable components. We present sharp lower and upper bounds on various dispersion measures (in particular, variance and median absolute deviation) of the system lifetime, expressed in terms of the system signature and the dispersion of a single component lifetime. We construct joint exchangeable distributions of component lifetimes with two-point marginals which attain the bounds in the limit.
On the Exponential Ergodicity of Lévy-Driven Ornstein–Uhlenbeck Processes
Authors: Wang Jian
Published: March 2016

Based on the explicit coupling property, the ergodicity and the exponential ergodicity of Lévy-driven Ornstein–Uhlenbeck processes are established.
Spectrally Negative Lévy Processes Perturbed by Functionals of their Running Supremum
Authors: Kyprianou Andreas E. , Ott Curdin
Published: March 2016

In the setting of the classical Cramér–Lundberg risk insurance model, Albrecher and Hipp (2007) introduced the idea of tax payments. More precisely, if X = {X

t
: t≥ 0} represents the Cramér–Lundberg process and, for all t≥ 0, S

t
=sup_{s≤ t}X

s
, then Albrecher and Hipp studied X

t
- γ S

t
,t≥ 0, where γ∈(0,1) is the rate at which tax is paid. This model has been generalised to the setting that X is a spectrally negative Lévy process by Albrecher, Renaud and Zhou (2008). Finally, Kyprianou and Zhou (2009) extended this model further by allowing the rate at which tax is paid with respect to the process S = {S

t
: t≥ 0} to vary as a function of the current value of S. Specifically, they considered the so-called perturbed spectrally negative Lévy process, U

t
:=X

t
-∫(0,t]γ(S_u)dS

u
,t≥ 0, under the assumptions that γ:[0,∞)→ [0,1) and ∫0
∞ (1-γ(s))d s =∞. In this article we show that a number of the identities in Kyprianou and Zhou (2009) are still valid for a much more general class of rate functions γ:[0,∞)→∝. Moreover, we show that, with appropriately chosen γ, the perturbed process can pass continuously (i.e. creep) into (-∞, 0) in two different ways.
Asymptotics of Maxima of Strongly Dependent Gaussian Processes
Authors: Tan Zhongquan , Hashorva Enkelejd , Peng Zuoxiang
Published: March 2016

Let {Xn(t),t∈[0,∞)},n∈ℕ, be standard stationary Gaussian processes. The limit distribution oft∈[0,T(n)]|Xn(t)| is established asrn(t), the correlation function of {Xn(t),t∈[0,∞)},n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).
A Glaser Twist: Focus on the Mixture Parameters
Authors: Block Henry W. , Langberg Naftali A. , Savits Thomas H.
Published: March 2016

In this paper we introduce a variation on Glaser's method for determining the shape of the failure rate function of a mixture. It has often been seen that the shape of the failure rate depends on the mixing parameter q. Our method provides an explanation for this phenomenon. We then illustrate our technique with the mixture of an exponential and a gamma density for all possible cases.
A Note on M/G/1 Vacation Systems with Sojourn Time Limits
Authors: Katayama Tsuyoshi
Published: March 2016

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in M/G/1 vacation systems with a general vacation time and two vacation rules.
Optimal Scaling of the Random Walk Metropolis: General Criteria for the 0.234 Acceptance Rule
Authors: Sherlock Chris
Published: March 2016

Scaling of proposals for Metropolis algorithms is an important practical problem in Markov chain Monte Carlo implementation. Analyses of the random walk Metropolis for high-dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the coordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary pth-order multivariate Markov process.
Asymptotics for the First Passage Times of Lévy Processes and Random Walks
Authors: Denisov Denis , Shneer Vsevolod
Published: March 2016

We study the exact asymptotics for the distribution of the first time, τ
x
, a Lévy process X

t
crosses a fixed negative level -x. We prove that ℙ{τ
x
>t} ~V(x) ℙ{X

t
≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τ
x
>t} explicitly in both light- and heavy-tailed cases.
Random Walks Reaching Against all Odds the other Side of the Quarter Plane
Authors: van Leeuwaarden Johan S. H. , Raschel Kilian
Published: March 2016

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state (i0,j0), we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive a certain integral representation for the probability of this event, and an asymptotic expression for the case wheni0becomes large, a situation in which the event becomes highly unlikely. The integral representation follows from the solution of a boundary value problem and involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model, and the asymmetric exclusion process.
Asymptotic Analysis of Hoppe Trees
Authors: Leckey Kevin , Neininger Ralph
Published: March 2016

We introduce and analyze a random tree model associated to Hoppe's urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node, where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight ϑ>0, a given fixed parameter, all other nodes have weight 1. This resembles the stochastic dynamic of Hoppe's urn. For ϑ=1, the resulting tree is the well-studied random recursive tree. We analyze the height, internal path length, and number of leaves of the Hoppe tree with n nodes as well as the depth of the last inserted node asymptotically as n→∞. Mainly expectations, variances, and asymptotic distributions of these parameters are derived.
Ancestral Graph with Bias in Gene Conversion
Authors: Mano Shuhei
Published: March 2016

Gene conversion is a genetic mechanism by which one gene is ‘copied and pasted’ onto another gene, where the direction can be biased between the different types. In this paper, a stochastic model for biased gene conversion within ad-unlinked multigene family and its diffusion approximation are developed for a finite Moran population. A connection with ad-island model is made. A formula for the fixation probability in the absence of mutation is given. A two-timescale argument is applied in the case of the strong conversion limit. The dual process is generally shown to be a biased voter model, which generates an ancestral bias graph for a given sample. An importance sampling algorithm for computing the likelihood of the sample is deduced.
A Duality Relation Between the Workload and Attained Waiting Time in FCFS G/G/s Queues
Authors: Yao Yi-Ching
Published: March 2016

Sengupta (1989) showed that, for the first-come–first-served (FCFS) G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. Sakasegawa and Wolff (1990) derived a sample path version of this result, showing that the empirical distribution of the workload values over a busy period of a given sample path is identical to that of the attained waiting time values over the same period. For a given sample path of an FCFS G/G/s queue, we construct a dual sample path of a dual queue which is FCFS G/G/s in reverse time. It is shown that the workload process on the original sample path is identical to the total attained waiting time process on the dual sample path. As an application of this duality relation, we show that, for a time-stationary FCFS M/M/s/k queue, the workload process is equal in distribution to the time-reversed total attained waiting time process.
The Minimal Entropy Martingale Measure for Exponential Markov Chains
Authors: Lee Young , Rheinländer Thorsten
Published: March 2016

In this article we investigate the minimal entropy martingale measure for continuous-time Markov chains. The conditions for absence of arbitrage and existence of the minimal entropy martingale measure are discussed. Under this measure, expressions for the transition intensities are obtained. Differential equations for the arbitrage-free price are derived.
The Resolvent and Expected Local Times for Markov-Modulated Brownian Motion with Phase-Dependent Termination Rates
Authors: Breuer Lothar
Published: March 2016

We consider a Markov-modulated Brownian motion (MMBM) with phase-dependent termination rates, i.e. while in a phase i the process terminates with a constant hazard rate r

i
≥ 0. For such a process, we determine the matrix of expected local times (at zero) before termination and hence the resolvent. The results are applied to some recent questions arising in the framework of insurance risk. We further provide expressions for the resolvent and the local times at zero of an MMBM reflected at its infimum.
Randomly Reinforced Urn Designs with Prespecified Allocations
Authors: Aletti Giacomo , Ghiglietti Andrea , Paganoni Anna Maria
Published: March 2016

We construct a response adaptive design, described in terms of a two-color urn model, targeting fixed asymptotic allocations. We prove asymptotic results for the process of colors generated by the urn and for the process of its compositions. An application of the proposed urn model is presented in an estimation problem context.
On the Number of Turns in Reduced Random Lattice Paths
Authors: Jiang Yunjiang , Xu Weijun
Published: March 2016

We consider the tree-reduced path of a symmetric random walk on ℤ
d
. It is interesting to ask about the number of turns T
n in the reduced path after n steps. This question arises from inverting the signatures of lattice paths: T
n gives an upper bound of the number of terms in the signature needed to reconstruct a ‘random’ lattice path with n steps. We show that, when n is large, the mean and variance of T
n in the asymptotic expansion have the same order as n, while the lower-order terms are O(1). We also obtain limit theorems for T
n, including the large deviations principle, central limit theorem, and invariance principle. Similar techniques apply to other finite patterns in a lattice path.
Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes
Authors: Fujii Takayuki
Published: March 2016

In this paper we study nonparametric estimation problems for a class of piecewise-deterministic Markov processes (PDMPs). Borovkov and Last (2008) proved a version of Rice's formula for PDMPs, which explains the relation between the stationary density and the level crossing intensity. From a statistical point of view, their result suggests a methodology for estimating the stationary density from observations of a sample path of PDMPs. First, we introduce the local time related to the level crossings and construct the local-time estimator for the stationary density, which is unbiased and uniformly consistent. Secondly, we investigate other estimation problems for the jump intensity and the conditional jump size distribution.