396 research outputs found
Levy Approximation of Impulsive Recurrent Process with Semi-Markov Switching
In this paper, the weak convergence of impulsive recurrent process with
semi-Markov switching in the scheme of Levy approximation is proved. Singular
perturbation problem for the compensating operator of the extended Markov
renewal process is used to prove the relative compactness
Gravity-Inspired Graph Autoencoders for Directed Link Prediction
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged
as powerful node embedding methods. In particular, graph AE and VAE were
successfully leveraged to tackle the challenging link prediction problem,
aiming at figuring out whether some pairs of nodes from a graph are connected
by unobserved edges. However, these models focus on undirected graphs and
therefore ignore the potential direction of the link, which is limiting for
numerous real-life applications. In this paper, we extend the graph AE and VAE
frameworks to address link prediction in directed graphs. We present a new
gravity-inspired decoder scheme that can effectively reconstruct directed
graphs from a node embedding. We empirically evaluate our method on three
different directed link prediction tasks, for which standard graph AE and VAE
perform poorly. We achieve competitive results on three real-world graphs,
outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management
(CIKM 2019
Diffusion Approximation with Equilibrium for Evolutionary Systems Switched by Semi-Markov Processes
We consider an evolutionary system switched by a semi-Markov process. For this system, we obtain an inhomogeneous diffusion approximation results where the initial process is compensated by the averaging function in the average approximation scheme.Для систем, що перемикаються иапівмарковськими процесами, одержано результати про неоднорідну дифузійну апроксимацію, де вихідний процес компенсується усередненою функцією в апроксимаційній схемі усереднення
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
A semi-Markov model with memory for price changes
We study the high frequency price dynamics of traded stocks by a model of
returns using a semi-Markov approach. More precisely we assume that the
intraday returns are described by a discrete time homogeneous semi-Markov which
depends also on a memory index. The index is introduced to take into account
periods of high and low volatility in the market. First of all we derive the
equations governing the process and then theoretical results have been compared
with empirical findings from real data. In particular we analyzed high
frequency data from the Italian stock market from first of January 2007 until
end of December 2010
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