bluuebunny/crossref_metadata_2025 huggingface dataset:
Conditional Limit Theorems for the Terms of a Random Walk Revisited
Authors: Bar-Lev Shaul K. , Schulte-Geers Ernst , Stadje Wolfgang
Published: March 2016

In this paper we derive limit theorems for the conditional distribution of X
1 given S

n
=s

n
as n→ ∞, where the X

i
are independent and identically distributed (i.i.d.) random variables, S

n
=X
1+··· +X

n
, and s

n
/n converges or s

n
≡ s is constant. We obtain convergence in total variation of P
X
1∣ S

n
/n=s
to a distribution associated to that of X
1 and of P
nX
1∣ S

n
=s
to a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.
A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm
Authors: Hong Dawei , Man Shushuang , Birget Jean-Camille , Lun Desmond S.
Published: March 2016

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1]of Hurst indexH∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM forH∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.
Random Construction of Interpolating Sets for High-Dimensional Integration
Authors: Huber Mark , Schott Sarah
Published: March 2016

Computing the value of a high-dimensional integral can often be reduced to the problem of finding the ratio between the measures of two sets. Monte Carlo methods are often used to approximate this ratio, but often one set will be exponentially larger than the other, which leads to an exponentially large variance. A standard method of dealing with this problem is to interpolate between the sets with a sequence of nested sets where neighboring sets have relative measures bounded above by a constant. Choosing such a well-balanced sequence can rarely be done without extensive study of a problem. Here a new approach that automatically obtains such sets is presented. These well-balanced sets allow for faster approximation algorithms for integrals and sums using fewer samples, and better tempering and annealing Markov chains for generating random samples. Applications, such as finding the partition function of the Ising model and normalizing constants for posterior distributions in Bayesian methods, are discussed.
Coalescence Times for the Bienaymé-Galton-Watson Process
Authors: Le V.
Published: March 2016

We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous-time Bienaymé-Galton-Watson process foundedtunits of time ago. We also obtain limiting distributions ast→ ∞ in the subcritical case. We extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.
Asymptotic Behaviour of Extinction Probability of Interacting Branching Collision Processes
Authors: Chen Anyue , Li Junping , Chen Yiqing , Zhou Dingxuan
Published: March 2016

Although the exact expressions for the extinction probabilities of the Interacting Branching Collision Processes (IBCP) were very recently given by Chen et al. [4], some of these expressions are very complicated; hence, useful information regarding asymptotic behaviour, for example, is harder to obtain. Also, these exact expressions take very different forms for different cases and thus seem lacking in homogeneity. In this paper, we show that the asymptotic behaviour of these extremely complicated and tangled expressions for extinction probabilities of IBCP follows an elegant and homogenous power law which takes a very simple form. In fact, we are able to show that if the extinction is not certain then the extinction probabilities {a

n
} follow an harmonious and simple asymptotic law of a

n
∼ kn
-αρ
c

n

as n → ∞, where k and α are two constants, ρ
c
is the unique positive zero of the C(s), and C(s) is the generating function of the infinitesimal collision rates. Moreover, the interesting and important quantity α takes a very simple and uniform form which could be interpreted as the ‘spectrum’, ranging from -∞ to +∞, of the interaction between the two components of branching and collision of the IBCP.
Pairs Trading with Opportunity Cost
Authors: Lindberg Carl
Published: March 2016

Pairs trading is a trading strategy which is used very frequently in the financial industry. An investment opportunity arises when the spread between two assets, which historically have exhibited autoregressive behavior, deviates from its recent history. In this case, the investor takes a long position in the asset which is expected to outperform going forward and finances this by taking a short position in the other one. If the spread converges, the investor can close both positions to generate a profit. We model the spread between two assets as an Ornstein-Uhlenbeck process and assume a constant opportunity cost. We then study the optimal liquidation strategy for an investor who wants to optimize profit in excess of the opportunity cost. Including this cost is important from an applied perspective, as the performance of any investment is always evaluated relative to the performance of the opportunity set.
Limit Theorems for Continuous-Time Branching Flows
Authors: He Hui , Ma Rugang
Published: March 2016

We construct a flow of continuous-time and discrete-state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses, over the positive half line, studied in Li (2014).
On Optimal Retirement
Authors: Ernst Philip A. , Foster Dean P. , Shepp Larry A.
Published: March 2016

We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function f and our current net worth X(t) for any t, we invest an amount f(X(t)) in the market. We need a fortune of M ‘superdollars’ to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Itô process dX(t) = (1 + f(X(t)))dt + f(X(t))dW(t). We show how to choose the optimal f = f
0 and show that the choice of f
0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.
Simulation Analysis of System Life when Component Lives are Determined by a Marked Point Process
Authors: Ross Sheldon M.
Published: March 2016

We consider an r component system having an arbitrary binary monotone structure function. We suppose that shocks occur according to a point process and that, independent of what has already occurred, each new shock is one of r different types, with respective probabilities p
1, …, p
r
. We further suppose that there are given integers n
1, …, n
r
such that component i fails (and remains failed) when there have been a total of n

i
type-i shocks. Letting L be the time at which the system fails, we are interested in using simulation to estimate E[L], E[L
2], and P(L > t). We show how to efficiently accomplish this when the point process is (i) a Poisson, (ii) a renewal, and (iii) a Hawkes process.
Improved Approximation of the Sum of Random Vectors by the Skew Normal Distribution
Authors: Christiansen Marcus C. , Loperfido Nicola
Published: March 2016

We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of n independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 at a rate of n
-2/3. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and n is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.
Parameter Dependent Optimal Thresholds, Indifference Levels and Inverse Optimal Stopping Problems
Authors: Klimmek Martin
Published: March 2016

Consider the classic infinite-horizon problem of stopping a one-dimensional diffusion to optimise between running and terminal rewards, and suppose that we are given a parametrised family of such problems. We provide a general theory of parameter dependence in infinite-horizon stopping problems for which threshold strategies are optimal. The crux of the approach is a supermodularity condition which guarantees that the family of problems is indexable by a set-valued map which we call the indifference map. This map is a natural generalisation of the allocation (Gittins) index, a classical quantity in the theory of dynamic allocation. Importantly, the notion of indexability leads to a framework for inverse optimal stopping problems.
A Characterisation of Transient Random Walks on Stochastic Matrices with Dirichlet Distributed Limits
Authors: McKinlay S.
Published: March 2016

We characterise the class of distributions of random stochastic matrices X with the property that the products X(n)X(n - 1) · · · X(1) of independent and identically distributed copies X(k) of X converge almost surely as n → ∞ and the limit is Dirichlet distributed. This extends a result by Chamayou and Letac (1994) and is illustrated by several examples that are of interest in applications.
A New Two-Urn Model
Authors: Chen May-Ru , Hsiau Shoou-Ren , Yang Ting-Hsin
Published: March 2016

We propose a two-urn model of Pólya type as follows. There are two urns, urn A and urn B. At the beginning, urn A contains r

A
red and w

A
white balls and urn B contains r

B
red and w

B
white balls. We first draw m balls from urn A and note their colors, say i red and m - i
white balls. The balls are returned to urn A and bi red and b(m - i) white balls are added to urn B. Next, we draw ℓ balls from urn B and note their colors, say j red and ℓ - j white balls. The balls are returned to urn B and aj red and a(ℓ - j) white balls are added to urn A. Repeat the above action n times and let X

n
be the fraction of red balls in urn A and Y

n
the fraction of red balls in urn B. We first show that the expectations of X

n
and Y

n
have the same limit, and then use martingale theory to show that X

n
and Y

n
converge almost surely to the same limit.
Uniqueness and Decay Properties of Markov Branching Processes with Disasters
Authors: Chen Anyue , Ng Kai Wang , Zhang Hanjun
Published: March 2016

In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest, we obtain the exact value of the decay parameter λ
C
. We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λ
C
-positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.
Comparison Results for GARCH Processes
Authors: Bellini Fabio , Pellerey Franco , Sgarra Carlo , Yasaei Sekeh Salimeh
Published: March 2016

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.
On Stationary Distributions of Stochastic Neural Networks
Authors: Borovkov K. , Decrouez G. , Gilson M.
Published: March 2016

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finite-dimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the components of the state space, and find upper bounds for them. For the density components, we derive a system of differential equations that can be solved in a few simplest cases only. Approaches to approximate computation of the stationary density are discussed. One approach is to reduce the dimensionality of the problem by modifying the network so that each neuron cannot fire if the number of spikes it emitted within the post-synaptic transfer kernel memory span reaches a given threshold. We show that the stationary distribution of this ‘truncated’ network converges to that of the unrestricted network as the threshold increases, and that the convergence is at a superexponential rate. A complementary approach uses discrete Markov chain approximations to the network process.
Investing and Stopping
Authors: Duembgen Moritz , Rogers L. C. G.
Published: March 2016

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.
Average Optimality for Continuous-Time Markov Decision Processes Under Weak Continuity Conditions
Authors: Zhang Yi
Published: March 2016

This paper considers the average optimality for a continuous-time Markov decision process in Borel state and action spaces, and with an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is proved under the conditions that allow the following; the controlled process can be explosive, the transition rates are weakly continuous, and the multifunction defining the admissible action spaces can be neither compact-valued nor upper semicontinuous.
A Binomial Splitting Process in Connection with Corner Parking Problems
Authors: Fuchs Michael , Hwang Hsien-Kuei , Itoh Yoshiaki , Mahmoud Hosam H.
Published: March 2016

This paper studies a special type of binomial splitting process. Such a process can be used to model a high dimensional corner parking problem as well as determining the depth of random PATRICIA (practical algorithm to retrieve information coded in alphanumeric) tries, which are a special class of digital tree data structures. The latter also has natural interpretations in terms of distinct values in independent and identically distributed geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by a logarithmic mean and a bounded variance, which is oscillating, if the binomial parameter p is not equal to ½, and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.
A Quenched Central Limit Theorem for Reversible Random Walks in a Random Environment on Z
Authors: Lam Hoang-Chuong
Published: March 2016

The main aim of this paper is to prove the quenched central limit theorem for reversible random walks in a stationary random environment on Z without having the integrability condition on the conductance and without using any martingale. The method shown here is particularly simple and was introduced by Depauw and Derrien [3]. More precisely, for a given realization ω of the environment, we consider the Poisson equation (P
ω - I)g = f, and then use the pointwise ergodic theorem in [8] to treat the limit of solutions and then the central limit theorem will be established by the convergence of moments. In particular, there is an analogue to a Markov process with discrete space and the diffusion in a stationary random environment.
Dirichlet Random Walks
Authors: Letac Gérard , Piccioni Mauro
Published: March 2016

This paper provides tools for the study of the Dirichlet random walk inRd. We compute explicitly, for a number of cases, the distribution of the random variableWusing a form of Stieltjes transform ofWinstead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process. We introduce the ideas of Dirichlet semigroups and Dirichlet infinite divisibility and characterize these infinite divisible distributions in the sense of Dirichlet when they are concentrated on the unit sphere ofRd.
The Euler Scheme for a Stochastic Differential Equation Driven by Pure Jump Semimartingales
Authors: Wang Hanchao
Published: March 2016

In this paper we propose the asymptotic error distributions of the Euler scheme for a stochastic differential equation driven by Itô semimartingales. Jacod (2004) studied this problem for stochastic differential equations driven by pure jump Lévy processes and obtained quite sharp results. We extend his results to a more general pure jump Itô semimartingale.
Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching
Authors: Jiang Zhengjun
Published: March 2016

In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Jiang and Pistorius [15] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.
Ergodic Inequality of a Two-Parameter Infinitely-Many-Alleles Diffusion Model
Authors: Zhou Youzhou
Published: March 2016

In this paper three models are considered. They are the infinitely-many-neutral-alleles model of Ethier and Kurtz (1981), the two-parameter infinitely-many-alleles diffusion model of Petrov (2009), and the infinitely-many-alleles model with symmetric dominance Ethier and Kurtz (1998). New representations of the transition densities are obtained for the first two models and the ergodic inequalities are provided for all three models.
A Limit Theorem for a Weiss Epidemic Process
Authors: Kalinkin A. V. , Mastikhin A. V.
Published: March 2016

For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.
New Results for the Two-Stage Contact Process
Authors: Foxall Eric
Published: March 2016

In this paper, we continue the work started by Steve Krone on the two-stage contact process. We give a simplified proof of the duality relation and answer most of the open questions posed in Krone (1999). We also fill in the details of an incomplete proof.
An Optimal Threshold Strategy in the Two-Envelope Problem with Partial Information
Authors: Egozcue Martin , Fuentes García Luis
Published: March 2016

In this paper we propose a strategy that gives an optimal lower bound of the average gain for the two-envelope problem within the McDonnell and Abbott (2009) and McDonnell et al. (2011) framework. We obtain this result with partial information about the probability distribution of the envelope's contents.
Functional Relationships Between Price and Volatility Jumps and Their Consequences for Discretely Observed Data
Authors: Jacod Jean , Klüppelberg Claudia , Müller Gernot
Published: March 2016

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein–Uhlenbeck and other continuous-time CARMA models as well as continuous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functionals of price and volatility processes for discrete observations of the price process on a grid, which are relevant for estimation and testing problems.
Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments
Authors: Hao Xuemiao , Tang Qihe
Published: March 2016

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y
0=x > 0, evolves according to dY

t
= Y

t- dR

t
-dP

t
for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x→∞, which confirms Paulsen's conjecture.
Berry–Esseen Bounds and the Law of the Iterated Logarithm for Estimators of Parameters in an Ornstein–Uhlenbeck Process with Linear Drift
Authors: Jiang Hui
Published: March 2016

We study the asymptotic behaviors of estimators of the parameters in an Ornstein–Uhlenbeck process with linear drift, such as the law of the iterated logarithm (LIL) and Berry–Esseen bounds. As an application of the Berry–Esseen bounds, the precise rates in the LIL for the estimators are obtained.
Approximating Quasistationary Distributions of Birth–Death Processes
Authors: Clancy Damian
Published: March 2016

For a sequence of finite state space birth–death processes, each having a single absorbing state, we show that, under certain conditions, as the size of the state space tends to infinity, the quasistationary distributions converge to the stationary distribution of a limiting infinite state space birth–death process. This generalizes a result of Keilson and Ramaswamy by allowing birth and death rates to depend upon the size of the state space. We give sufficient conditions under which the convergence result of Keilson and Ramaswamy remains valid. The generalization allows us to apply our convergence result to examples from population biology: a Pearl–Verhulst logistic population growth model and the susceptible-infective-susceptible (SIS) model for infectious spread. The limit distributions obtained suggest new finite-population approximations to the quasistationary distributions of these models, obtained by the method of cumulant closure. The new approximations are found to be both simple in form and accurate.
Optimal Sequential Change Detection for Fractional Diffusion-Type Processes
Authors: Chronopoulou Alexandra , Fellouris Georgios
Published: March 2016

The problem of detecting an abrupt change in the distribution of an arbitrary, sequentially observed, continuous-path stochastic process is considered and the optimality of the CUSUM test is established with respect to a modified version of Lorden's criterion. We apply this result to the case that a random drift emerges in a fractional Brownian motion and we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst indexHadopts a polynomial drift term with exponentH+1/2.
Domain of Attraction of the Quasistationary Distribution for Birth-and-Death Processes
Authors: Zhang Hanjun , Zhu Yixia
Published: March 2016

We consider a birth–death process {X(t),t≥0} on the positive integers for which the origin is an absorbing state with birth coefficients λ
n
,n≥0, and death coefficients μ
n
,n≥0. If we define A=∑
n=1
∞ 1/λ
n
π
n
and S=∑
n=1
∞ (1/λ
n
π
n
)∑
i=n+1
∞ π
i
, where {π
n
,n≥1} are the potential coefficients, it is a well-known fact (see van Doorn (1991)) that if A=∞ and S<∞, then λ
C
>0 and there is precisely one quasistationary distribution, namely, {a

j
(λ
C
)}, where λ
C
is the decay parameter of {X(t),t≥0} in C={1,2,...} and a

j
(x)≡μ1
-1π
j

xQ

j
(x), j=1,2,.... In this paper we prove that there is a unique quasistationary distribution that attracts all initial distributions supported in C, if and only if the birth–death process {X(t),t≥0} satisfies bothA=∞ and S<∞. That is, for any probability measure M={m

i
, i=1,2,...}, we have lim
t→∞ℙ
M
(X(t)=j∣ T>t)= a

j
(λ
C
), j=1,2,..., where T=inf{t≥0 : X(t)=0} is the extinction time of {X(t),t≥0} if and only if the birth–death process {X(t),t≥0} satisfies both A=∞ and S<∞.
Conditional Distributions of Processes Related to Fractional Brownian Motion
Authors: Fink Holger , Klüppelberg Claudia , Zähle Martina
Published: March 2016

Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.
Splitting Trees Stopped when the First Clock Rings and Vervaat's Transformation
Authors: Lambert Amaury , Trapman Pieter
Published: March 2016

We consider a branching population where individuals have independent and identically distributed (i.i.d.) life lengths (not necessarily exponential) and constant birth rates. We let N

t
denote the population size at time t. We further assume that all individuals, at their birth times, are equipped with independent exponential clocks with parameter δ. We are interested in the genealogical tree stopped at the first time T when one of these clocks rings. This question has applications in epidemiology, population genetics, ecology, and queueing theory. We show that, conditional on {T<∞}, the joint law of (N

t
, T, X
(T)), where X
(T) is the jumping contour process of the tree truncated at time T, is equal to that of (M, -I

M
, Y′

M
) conditional on {M≠0}. Here M+1 is the number of visits of 0, before some single, independent exponential clock
e
with parameter δ rings, by some specified Lévy process Y without negative jumps reflected below its supremum; I

M
is the infimum of the path Y

M
, which in turn is defined as Y killed at its last visit of 0 before
e
; and Y′

M
is the Vervaat transform of Y

M
. This identity yields an explanation for the geometric distribution of N

T
(see Kitaev (1993) and Trapman and Bootsma (2009)) and has numerous other applications. In particular, conditional on {N

T
=n}, and also on {N

T
=n,T<a}, the ages and residual lifetimes of the n alive individuals at time T are i.i.d. and independent of n. We provide explicit formulae for this distribution and give a more general application to outbreaks of antibiotic-resistant bacteria in the hospital.
Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics
Authors: Burkschat M. , Navarro J.
Published: March 2016

Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.
From Hermite Polynomials to Multifractional Processes
Authors: Marty Renaud
Published: March 2016

We consider a class of multifractional processes related to Hermite polynomials. We show that these processes satisfy an invariance principle. To prove the main result of this paper, we use properties of the Hermite polynomials and the multiple Wiener integrals. Because of the multifractionality, we also need to deal with variations of the Hurst index by means of some uniform estimates.
Asian Options Under One-Sided Lévy Models
Authors: Patie P.
Published: March 2016

We generalize, in terms of power series, the celebrated Geman-Yor formula for the pricing of Asian options in the framework of spectrally negative Lévy-driven assets. We illustrate our result by providing some new examples.
Stochastic Boundary Crossing Probabilities for the Brownian Motion
Authors: Che Xiaonan , Dassios Angelos
Published: March 2016

Using martingale methods, we derive a set of theorems of boundary crossing probabilities for a Brownian motion with different kinds of stochastic boundaries, in particular compound Poisson process boundaries. We present both the numerical results and simulation experiments. The paper is motivated by limits on exposure of UK banks set by CHAPS. The central and participating banks are interested in the probability that the limits are exceeded. The problem can be reduced to the calculation of the boundary crossing probability from a Brownian motion with stochastic boundaries. Boundary crossing problems are also very popular in many fields of statistics.
Pruned Discrete Random Samples
Authors: Grübel Rudolf , Hitczenko Paweł
Published: March 2016

Let X

i
,i ∈ ℕ, be independent and identically distributed random variables with values in ℕ0. We transform (‘prune’) the sequence {X
1,…,X

n
},n∈ ℕ, of discrete random samples into a sequence {0,1,2,…,Y

n
}, n∈ ℕ, of contiguous random sets by replacing X

n+1 with Y

n
+1 if X

n+1 >Y

n
. We consider the asymptotic behaviour of Y

n
as n→∞. Applications include path growth in digital search trees and the number of tables in Pitman's Chinese restaurant process if the latter is conditioned on its limit value.
Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time
Authors: Hu Yaozhong , Lee Chihoon
Published: March 2016

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.
Comparison of Cutoffs Between Lazy Walks and Markovian Semigroups
Authors: Chen Guan-Yu , Saloff-Coste Laurent
Published: March 2016

We make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a criterion on cutoffs using eigenvalues of the transition matrix.
On the Modelling of Imperfect Repairs for a Continuously Monitored Gamma Wear Process Through Age Reduction
Authors: Mercier Sophie , Castro I. T.
Published: March 2016

A continuously monitored system is considered, which is subject to accumulating deterioration modelled as a gamma process. The system fails when its degradation level exceeds a limit threshold. At failure, a delayed replacement is performed. To shorten the down period, a condition-based maintenance strategy is applied, with imperfect repair. Mimicking virtual age models used for recurrent events, imperfect repair actions are assumed to lower the system degradation through a first-order arithmetic reduction of age model. Under these assumptions, Markov renewal equations are obtained for several reliability indicators. Numerical examples illustrate the behaviour of the system.
Optimal Coadapted Coupling for a Random Walk on the Hyper-Complete Graph
Authors: Connor Stephen
Published: March 2016

The problem of constructing an optimal coadapted coupling for a pair of symmetric random walks onZ2dwas considered by Connor and Jacka (2008), and the existence of a coupling which is stochastically fastest in the class of all such coadapted couplings was demonstrated. In this paper we show how to generalise this construction to an optimal coadapted coupling for the continuous-time symmetric random walk onKnd, whereKnis the complete graph withnvertices. Moreover, we show that although this coupling is not maximal for anyn(i.e. it does not achieve equality in the coupling inequality), it does tend to a maximal coupling asn→ ∞.
Upper Bounds for the Maximum of a Random Walk with Negative Drift
Authors: Kugler Johannes , Wachtel Vitali
Published: March 2016

Consider a random walk S

n
= ∑
i=0

n

X

i
with negative drift. This paper deals with upper bounds for the maximum M = max
n≥1
S

n
of this random walk in different settings of power moment existences. As is usual for deriving upper bounds, we truncate summands. Therefore, we use an approach of splitting the time axis by stopping times into intervals of random but finite length and then choose a level of truncation on each interval. Hereby, we can reduce the problem of finding upper bounds for M to the problem of finding upper bounds for M
τ = max
n≤τ
S

n
. In addition we test our inequalities in the heavy traffic regime in the case of regularly varying tails.
On Generalized Pólya Urn Models
Authors: Chen May-Ru , Kuba Markus
Published: March 2016

We study an urn model introduced in the paper of Chen and Wei (2005), where at each discrete time step m balls are drawn at random from the urn containing colors white and black. Balls are added to the urn according to the inspected colors, generalizing the well known Pólya-Eggenberger urn model, case m = 1. We provide exact expressions for the expectation and the variance of the number of white balls after n draws, and determine the structure of higher moments. Moreover, we discuss extensions to more than two colors. Furthermore, we introduce and discuss a new urn model where the sampling of the m balls is carried out in a step-by-step fashion, and also introduce a generalized Friedman's urn model.
General inverse problems for regular variation
Authors: Damek Ewa , Mikosch Thomas , Rosiński Jan , Samorodnitsky Gennady
Published: March 2016

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build on previous work, and derive results in the multivariate case and in situations where regular variation is not restricted to one particular direction or quadrant.
Partially informed investors: hedging in an incomplete market with default
Authors: Tardelli P.
Published: March 2016

In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements, the risky asset prices are modelled by marked point processes. Their dynamics depend on an unobservable process, representing the amount of news reaching the market. This is a marked point process, which may have common jump times with the risky asset price processes. The problem of hedging a defaultable claim is studied. In order to discuss all these topics, in this paper we examine stochastic control problems using backward stochastic differential equations (BSDEs) and filtering techniques. The goal of this paper is to construct a sequence of functions converging to the value function, each of these is the unique solution of a suitable BSDE.
Occurrence of the Endangered Antillean manatee Trichechus manatus manatus in a marine protected area, Isla de la Juventud, Cuba
Authors: Alvarez-Alemán Anmari , Angulo-Valdés Jorge A. , García Alfonso Eddy , Powell James A. , Taylor Cynthia R.
Published: March 2016

The Antillean manatee Trichechus manatus manatus is categorized as Endangered on the IUCN Red List but little is known about the status of the species in Cuba. Marine protected areas can contribute to manatee conservation in Cuba but the effectiveness of these areas may be jeopardized by a lack of information regarding appropriate design and management. We developed an index of manatee occurrence in the Fauna Refuge Ciénaga de Lanier, Isla de la Juventud, to assess patterns of manatee use in the reserve. We completed 26 field trips during November 2007–October 2013, with a total of 147 survey days. Manatee presence was detected on 47% of survey days and in 96% of field trips; 133 individuals were recorded in 93 sightings. The index of manatee occurrence varied between trips, suggesting a discontinuous use of the area. The mean group size was 1.4 individuals (range 1–5), and calves were observed in 13% of sightings. Observations of manatee behaviour, occurrence and habitat characteristics indicate the importance of the study area as a resting place, refuge and source of fresh water. We recommend that manatee protection be strengthened to avoid human-related mortality and to ensure that the habitats that provide critical resources are given special consideration in future management plans.
The effect of implicit causality and consequentiality on nonnative pronoun resolution
Authors: CHENG WEI , ALMOR AMIT
Published: March 2016

We report two sentence-completion experiments investigating how nonnative speakers use universal semantic and discourse information, which are implicit causality and consequentiality biases associated with psychological verbs, to resolve pronouns. The results indicate that intermediate-advanced and advanced Chinese-speaking English learners show weaker implicit causality and consequentiality biases than native English speakers in pronoun resolution. Instead, nonnative speakers exhibit a general subject or first-mention bias. These findings suggest that nonnative speakers do not use semantic and discourse information in comprehension as effectively as native speakers.
Job creation and firm-specific location incentives
Authors: Jensen Nathan M.
Published: March 2016

Government economic development programmes provide opportunities for firms to leverage financial incentives for business expansion and relocation. This article examines the ability of these incentives to promote employment. Using establishment-level data from the state of Kansas as well as original firm-level survey data, I evaluate the effectiveness of financial incentives in creating jobs through recipient firms. My findings from the establishment-level data indicate that incentive programmes have no discernable impact on firm expansion, measured by job creation. In addition, the survey data suggest that incentive recipients highly recommend this programme to other firms, but few firms actually increased their employment in Kansas because of these incentives; similarly, very few firms would have left the state if they had not benefited from this programme. Thus, incentives have little impact on the relocation or expansion decisions of firms.
Donors and the Global Sportive “Civilizing Mission”: Asian Athletics, American Philanthropy, and YMCA Media (1910s–1920s)
Authors: Hübner Stefan
Published: March 2016

This article focuses on changes in American philanthropy during the Progressive Era and the Young Men’s Christian Association’s (YMCA) domestic promotion of its global sports program during the 1910s and 1920s. Since the American YMCA’s foreign department was entirely dependent on donations, philanthropists’ demands concerning efficient and scientific methods to fight the causes of social dysfunction needed to be addressed. YMCA and Christian progressive media thus presented clear-cut success stories about spreading Western sports. Oft-repeated topoi included the superiority vis-à-vis local practices of Western scientific and rational approaches to public health and leisure, and a knowledge transfer to local elites, meaning that indigenization would prevent a permanent “donation drain.” During the First World War, Asian sports events were communicated as a peaceful contrast to the European battlefields. Following the war, YMCA writers turned Asian athletes into a vanguard among non-Western athletes, now promoting the YMCA’s experience gained in this region as a guarantee to donors that an expensive expansion of its sportive “civilizing mission” would lead to similar achievements on a global level. By the late 1920s, the YMCA had completely “de-Orientalized” its earlier coverage of Asian social deficits to emphasize its own efficiency.
The Nationalization of Lonrho’s Business Interests in Postcolonial Tanzania
Authors: Uche Chibuike
Published: March 2016

On June 2, 1978, the Tanzanian government under President Julius Nyerere ordered the British multinational corporation, Lonrho Limited, to leave the country. The “official reason” provided for this action was Lonrho’s “continued defiance of the United Nations mandatory sanctions against Rhodesia and the expansion of its business interests in South Africa.” Using newly available materials, mainly from the National Archives London, this paper attempts to document the rise of Lonrho in Tanzania up until the nationalization, the factors that influenced the compensation negotiations process between Lonrho and the Tanzanian government, and the role the British government played in the entire episode.
Task-Based Versus Task-Supported Language Instruction: An Experimental Study
Authors: Li Shaofeng , Ellis Rod , Zhu Yan
Published: March 2016

This study investigated the effectiveness of task-based and task-supported instruction in the acquisition of the English passive construction—a structure about which learners had limited prior knowledge. A total of 150 Chinese middle school English as a foreign language (EFL) learners were randomly assigned to five groups—one control group who only took the pretest and posttests and four experimental groups who attended a 2-hour treatment session where they performed two dictogloss tasks in groups, each including a reporting phase when the learners took turns to tell the narrative. Among the four experimental groups, one just performed the two oral tasks; a second group received explicit instruction before performing the tasks; a third group received within-task feedback but no explicit instruction; and the fourth group received both explicit instruction and within-task feedback. Treatment effects were gauged via a grammaticality judgment test (GJT) and an elicited imitation test (EIT). On the GJT, the conditions with explicit instruction and/or feedback led to significant gains with explicit instruction plus feedback showing the largest effects. On the EIT, there was no effect for any of the three treatment groups when the data were analyzed for the whole cohort. However, when the learners were subdivided into those with zero and some prior knowledge based on their pretest EIT scores, explicit instruction plus within-task feedback was more effective than the other treatment types for the latter.
Towards an Improvement of Magnetic Compass Accuracy and Adjustment
Authors: Basterretxea-Iribar Imanol , Sotés Iranzu , Uriarte Jose Ignacio
Published: March 2016

Many ship accidents have arisen from an error in course indication. Bearing in mind that the actual errors in gyrocompass and satellite compass are really minor, they may be considered valid to be input into an autopilot provided that any failure in such devices is controlled by means of a secondary heading source such as a magnetic compass. However, magnetic compass deviation may be significant and its heading should be corrected before being input to the autopilot. The errors caused by the geographic variability of the deviation should also be taken into account. Moreover, the current way to reduce the deviation requires that the ship is un-berthed to execute a complete swing. The aim of this article is to obtain a ship magnetic model by means of an algorithm based on least squares to correct magnetic compass heading input in the autopilot and to permit definitive magnetic compass compensation without swinging the ship through 360°.
Driving Task: How Older Drivers’ On-Road Driving Performance Relates to Abilities, Perceptions, and Restrictions
Authors: Koppel Sjaan , Charlton Judith L. , Langford Jim , Di Stefano Marilyn , MacDonald Wendy , Vlahodimitrakou Zafiroula , Mazer Barbara L. , Gelinas Isabelle , Vrkljan Brenda , Eliasz Kinga , Myers Anita , Tuokko Holly A. , Marshall Shawn C.
Published: March 2016

Cette étude a examiné une cohorte de 227 conducteurs âgés et a étudié la relation entre leur performance sur la grille d’observation e-DOS pour manœuvres de conduite et (1) les caractéristiques des conducteurs; (2) les capacités fonctionnelles; (3) les perceptions des capacités et le confort pendant la conduite, ainsi que (4) les restrictions auto-déclarées de la conduite. Les participants (hommes: 70%; âge: M = 81.53 ans, É-T = 3,37 ans) a achevé une série de mesures de la capacité fonctionnelle et d’écailles sur le confort, les capacités et les restrictions aperçut du Candrive / Ozcandrive protocole d’évaluation Année 2, avec une tâche de conduite e-DOS. Les observations des comportements de conduite des participants au cours de la tâche de conduite ont été enregistrées pour : la négociation au carrefour, le changement de voie, la fusion, les manœuvres à basse vitesse, et la conduite sans manoeuvres. Les scores de conduite e-DOS étaient élevés (M = 94,74; É-T = 5,70) et étaient liés d’une façon significative aux capacité de conduite perçu des participants, la fréquence rapporté de la conduite dans des situations difficiles, et le nombre de restrictions de la conduite. Les analyses futures exploreront les changements potentiels dans les scores de tâches de conduite au fil du temps.