370 research outputs found
On the Limit Distributions of Continuous-State Branching Processes with Immigration
We consider the class of continuous-state branching processes with
immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) and their
limit distributions as time tends to infinity. We determine the Levy-Khintchine
triplet of the limit distribution and give an explicit description in terms of
the characteristic triplets of the Levy subordinator and the spectrally
positive Levy process, which describe the immigration resp. branching mechanism
of the CBI-process. This representation allows us to describe the support of
the limit distribution and characterise its absolute continuity and asymptotic
behavior at the boundary of the support, generalizing several known results on
self-decomposable distributions.Comment: minor update; to appear in SP
First and second order semi-Markov chains for wind speed modeling
The increasing interest in renewable energy, particularly in wind, has given
rise to the necessity of accurate models for the generation of good synthetic
wind speed data. Markov chains are often used with this purpose but better
models are needed to reproduce the statistical properties of wind speed data.
We downloaded a database, freely available from the web, in which are included
wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10
minutes. With the aim of reproducing the statistical properties of this data we
propose the use of three semi-Markov models. We generate synthetic time series
for wind speed by means of Monte Carlo simulations. The time lagged
autocorrelation is then used to compare statistical properties of the proposed
models with those of real data and also with a synthetic time series generated
though a simple Markov chain.Comment: accepted for publication on Physica
Choice-Based Demand Management and Vehicle Routing in E-Fulfillment
Attended home delivery services face the challenge of providing narrow delivery time slots to ensure customer satisfaction, while keeping the significant delivery costs under control. To that end, a firm can try to influence customers when they are booking their delivery time slot so as to steer them toward choosing slots that are expected to result in cost-effective schedules. We estimate a multinomial logit customer choice model from historic booking data and demonstrate that this can be calibrated well on a genuine e-grocer data set. We propose dynamic pricing policies based on this choice model to determine which and how much incentive (discount or charge) to offer for each time slot at the time a customer intends to make a booking. A crucial role in these dynamic pricing problems is played by the delivery cost, which is also estimated dynamically. We show in a simulation study based on real data that anticipating the likely future delivery cost of an additional order in a given location can lead to significantly increased profit as compared with current industry practice
Invariant, super and quasi-martingale functions of a Markov process
We identify the linear space spanned by the real-valued excessive functions
of a Markov process with the set of those functions which are quasimartingales
when we compose them with the process. Applications to semi-Dirichlet forms are
given. We provide a unifying result which clarifies the relations between
harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale
functions, showing that in the conservative case they are all the same.
Finally, using the co-excessive functions, we present a two-step approach to
the existence of invariant probability measures
The occupation of a box as a toy model for the seismic cycle of a fault
We illustrate how a simple statistical model can describe the quasiperiodic
occurrence of large earthquakes. The model idealizes the loading of elastic
energy in a seismic fault by the stochastic filling of a box. The emptying of
the box after it is full is analogous to the generation of a large earthquake
in which the fault relaxes after having been loaded to its failure threshold.
The duration of the filling process is analogous to the seismic cycle, the time
interval between two successive large earthquakes in a particular fault. The
simplicity of the model enables us to derive the statistical distribution of
its seismic cycle. We use this distribution to fit the series of earthquakes
with magnitude around 6 that occurred at the Parkfield segment of the San
Andreas fault in California. Using this fit, we estimate the probability of the
next large earthquake at Parkfield and devise a simple forecasting strategy.Comment: Final version of the published paper, with an erratum and an
unpublished appendix with some proof
Solvable non-Markovian dynamic network
Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result
Semi-Markov Graph Dynamics
In this paper, we outline a model of graph (or network) dynamics based on two
ingredients. The first ingredient is a Markov chain on the space of possible
graphs. The second ingredient is a semi-Markov counting process of renewal
type. The model consists in subordinating the Markov chain to the semi-Markov
counting process. In simple words, this means that the chain transitions occur
at random time instants called epochs. The model is quite rich and its possible
connections with algebraic geometry are briefly discussed. Moreover, for the
sake of simplicity, we focus on the space of undirected graphs with a fixed
number of nodes. However, in an example, we present an interbank market model
where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON
Linear independence of root equations for M/G /1 type Markov chains
There is a classical technique for determining the equilibrium probabilities of M/G/1 type Markov chains. After transforming the equilibrium balance equations of the chain, one obtains an equivalent system of equations in analytic functions to be solved. This method requires finding all singularities of a given matrix function in the unit disk and then using them to obtain a set of linear equations in the finite number of unknown boundary probabilities. The remaining probabilities and other measures of interest are then computed from the boundary probabilities. Under certain technical assumptions, the linear independence of the resulting equations is established by a direct argument involving only elementary results from matrix theory and complex analysis. Simple conditions for the ergodicity and nonergodicity of the chain are also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47619/1/11134_2005_Article_BF01245323.pd
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