Recursos de colección
Holst, Lars
In a sequence of independent Bernoulli trials the probability of
success in the kth trial is
p_{k} = a / (a + b + k - 1).
An explicit formula for the binomial moments of the number of two
consecutive successes in the first n trials is obtained and
some consequences of it are derived.
Mahmoud, Hosam M.; Ward, Mark Daniel
We investigate the average similarity of random strings as
captured by the average number of `cousins' in the underlying tree
structures. Analytical techniques including poissonization and the
Mellin transform are used for accurate calculation of the mean.
The string alphabets we consider are m-ary, and the
corresponding trees are m-ary trees. Certain analytic
issues arise in the m-ary case that do not have an analog
in the binary case.
Ebrahimi, Nader
Nanosystems are devices that are in the size range of a billionth
of a meter (1 x 10^{-9}) and therefore are built
necessarily from individual atoms. The one-dimensional nanosystems
or linear nanosystems cover all the nanosized systems which
possess one dimension that exceeds the other two dimensions, i.e.
extension over one dimension is predominant over the other two
dimensions. Here only two of the dimensions have to be on the
nanoscale (less than 100 nanometers). In this paper we consider
the structural relationship between a linear nanosystem and its
atoms acting as components of the nanosystem. Using such
information, we then assess the nanosystem's limiting reliability
which is, of course, probabilistic...
Daduna, Hans; Szekli, Ryszard
For exponential open and closed queueing networks, we investigate
the internal dependence structure, compare the internal dependence
for different networks, and discuss the relation of correlation
formulae to the existence of spectral gaps and comparison of
asymptotic variances. A central prerequisite for the derived
theorems is stochastic monotonicity of the networks. The
dependence structure of network processes is described by
concordance order with respect to various classes of functions.
Different networks with the same first-order characteristics are
compared with respect to their second-order properties. If a
network is perturbed by changing the routeing in a way which holds
the routeing equilibrium fixed, the resulting perturbations of the
network processes are evaluated.
Biagini, Francesca; Bregman, Yuliya; Meyer-Brandis, Thilo
We specify a model for a catastrophe loss index, where the initial
estimate of each catastrophe loss is reestimated immediately by a
positive martingale starting from the random time of loss
occurrence. We consider the pricing of catastrophe insurance
options written on the loss index and obtain option pricing
formulae by applying Fourier transform techniques. An important
advantage is that our methodology works for loss distributions
with heavy tails, which is the appropriate tail behavior for
catastrophe modeling. We also discuss the case when the
reestimation factors are given by positive affine martingales and
provide a characterization of positive affine local martingales.
Zhu, Jinxia; Yang, Hailiang
In this paper we consider a compound Poisson risk model where the
insurer earns credit interest at a constant rate if the surplus is
positive and pays out debit interest at another constant rate if
the surplus is negative. Absolute ruin occurs at the moment when
the surplus first drops below a critical value (a negative
constant). We study the asymptotic properties of the absolute ruin
probability of this model. First we investigate the asymptotic
behavior of the absolute ruin probability when the claim size
distribution is light tailed. Then we study the case where the
common distribution of claim sizes are heavy tailed.
Gao, Fuqing; Yan, Jun
We establish a functional large deviation principle and a
functional moderate deviation principle for Markov-modulated risk
models with reinsurance by constructing an exponential martingale
approach. Lundberg's estimate of the ruin time is also presented.
Breuer, Lothar
The present paper generalises some results for spectrally negative
Lévy processes to the setting of Markov additive processes
(MAPs). A prominent role is assumed by the first passage times,
which will be determined in terms of their Laplace transforms.
These have the form of a phase-type distribution, with a rate
matrix that can be regarded as an inverse function of the cumulant
matrix. A numerically stable iteration to compute this matrix is
given. The theory is first developed for MAPs without positive
jumps and then extended to include positive jumps having
phase-type distributions. Numerical and analytical examples show
agreement with existing results in special cases.
Kessler, David A.
We study the susceptible-infected-susceptible model of the spread
of an endemic infection. We calculate an exact expression for the
mean number of transmissions for all values of the population size
(N) and the infectivity. We derive the large-N
asymptotic behavior for the infectivitiy below, above, and in the
critical region. We obtain an analytical expression for the
probability distribution of the number of transmissions, n,
in the critical region. We show that this distribution has an
n^{-3/2} singularity for small n and decays
exponentially for large n. The exponent decreases with the
distance from the threshold, diverging to ∞ far below and
approaching 0 far above.
Britton, Tom; Deijfen, Maria; Lagerås, Andreas N.; Lindholm, Mathias
In this paper a branching process approximation for the spread of
a Reed-Frost epidemic on a network with tunable clustering is
derived. The approximation gives rise to expressions for the
epidemic threshold and the probability of a large outbreak in the
epidemic. We investigate how these quantities vary with the
clustering in the graph and find that, as the clustering
increases, the epidemic threshold decreases. The network is
modeled by a random intersection graph, in which individuals are
independently members of a number of groups and two individuals
are linked to each other if and only if there is at least one
group that they are both members of.
Piau, Didier
We compute the posterior distributions of the initial population
and parameter of binary branching processes in the limit of a
large number of generations. We compare this Bayesian procedure
with a more naïve one, based on hitting times of some
random walks. In both cases, central limit theorems are available,
with explicit variances.
Bertoin, Jean; Fontbona, Joaquin; Martínez, Servet
We describe the genealogy of individuals with infinite descent in
a supercritical continuous-state branching process.
Connor, Stephen; Jacka, Saul
Let X and Y be two simple symmetric continuous-time
random walks on the vertices of the n-dimensional
hypercube, Z_{2}^{n}. We consider
the class of co-adapted couplings of these processes, and describe
an intuitive coupling which is shown to be the fastest in this
class.
Comets, Francis; Simenhaus, François
We study a continuous-time random walk on the d-dimensional
lattice, subject to a drift and an attraction to large clusters of
a subcritical Bernoulli site percolation. We find two distinct
regimes: a ballistic one, and a subballistic one taking place when
the attraction is strong enough. We identify the speed in the
former case, and the algebraic rate of escape in the latter case.
Finally, we discuss the diffusive behavior in the case of zero
drift and weak attraction.
Jacka, Saul; Sheehan, Marcus
We study a particular example of a recursive distributional
equation (RDE) on the unit interval. We identify all invariant
distributions, the corresponding `basins of attraction', and
address the issue of endogeny for the associated tree-indexed
problem, making use of an extension of a recent result of Warren.
Ledoux, James; White, Langford B.; Brushe, Gary D.
The aim of this paper is to provide the conditions necessary to
reduce the complexity of state filtering for finite stochastic
systems (FSSs). A concept of lumpability for FSSs is introduced.
In this paper we assert that the unnormalised filter for a lumped
FSS has linear dynamics. Two sufficient conditions for such a
lumpability property to hold are discussed. We show that the first
condition is also necessary for the lumped FSS to have linear
dynamics. Next, we prove that the second condition allows the
filter of the original FSS to be obtained directly from the filter
for the lumped FSS. Finally, we generalise an earlier published
result for the...
de la Peña, Victor; Gzyl, Henryk; McDonald, Patrick
Let W_{n} be a simple Markov chain on the
integers. Suppose that X_{n} is a simple
Markov chain on the integers whose transition probabilities
coincide with those of W_{n} off a finite
set. We prove that there is an M > 0 such that the
Markov chain W_{n} and the joint
distributions of the first hitting time and first hitting place of
X_{n} started at the origin for the sets
{-M, M} and {-(M + 1), (M + 1)}
algorithmically determine the transition probabilities of
X_{n}.
Ruiz, Víctor
We introduce a class of stochastic processes in discrete time with
finite state space by means of a simple matrix product. We show
that this class coincides with that of the hidden Markov chains
and provides a compact framework for it. We study a measure
obtained by a projection on the real line of the uniform measure
on the Sierpinski gasket, finding that the dimension of this
measure fits with the Shannon entropy of an associated hidden
Markov chain.
Neal, Peter
Coupons are collected one at a time from a population containing
n distinct types of coupon. The process is repeated until
all n coupons have been collected and the total number of
draws, Y, from the population is recorded. It is assumed
that the draws from the population are independent and identically
distributed (draws with replacement) according to a probability
distribution X with the probability that a type-i
coupon is drawn being P(X = i). The special case
where each type of coupon is equally likely to be drawn from the
population is the classic coupon collector problem. We consider
the asymptotic distribution Y (appropriately normalized) as
the number of coupons...
Kella, Offer; Stadje, Wolfgang
We study a collector's problem with K renewal arrival
processes for different type items, where the objective is to
collect complete sets. In particular, we derive the asymptotic
distribution of the sequence of interarrival times between set
completions.