2,176 research outputs found
Local times for spectrally negative L\'evy processes
For spectrally negative L\'evy processes, adapting an approach from
\cite{BoLi:sub1} we identify joint
Laplace transforms involving local times evaluated at either the first
passage times, or independent exponential times, or inverse local times. The
Laplace transforms are expressed in terms of the associated scale functions.
Connections are made with the permanental process and the Markovian loop soup
measure.Comment: 23 page
Self-consistent Force Scheme in the Discrete Boltzmann Equation
In the work of N. Martys et al. [Nicos S. Martys, Xiaowen Shan, Hudong Chen,
Phys. Rev. E, Vol. 58, Num.5, 1998 ], a self-consistent force term to any order
in the Boltzmann-BKG equation is derived by the Hermite basis with raw
velocity. As an extension, in the present work, the force term is expanded by
the Hermite basis with the relative velocity in the comoving coordinate and the
Hermite basis with the relative velocity scaled by the local temperature. It is
found that the force scheme proposed by He et al. [Xiaoyi He, Xiaowen Shan,
Gary D. Doolen, Phys. Rev. E, Vol. 57, Num.1,1998] can be derived by the
Hermite basis with the relative velocity. Furthermore, another new force scheme
in which the velocity is scaled by the local temperature is obtained.Comment: this is a pure theoretical work associated with the force scheme for
the discrete Boltzmann equation. It has 7 pages, 0 figure. This work is
prepared to be submited to Physical Review serie
Integral functionals for spectrally positive Levy processes
We find necessary and sufficient conditions for almost sure finiteness of
integral functionals of spectrally positive L\'evy processes. Via Lamperti type
transforms, these results can be applied to obtain new integral tests on
extinction and explosion behaviors for a class of continuous-state nonlinear
branching processes
An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure
This paper concerns the almost sure time dependent local extinction behavior
for super-coalescing Brownian motion with -stable branching and
Lebesgue initial measure on \bR. We first give a representation of using
excursions of a continuous state branching process and Arratia's coalescing
Brownian flow. For any nonnegative, nondecreasing and right continuous function
, put
\tau:=\sup \{t\geq 0: X_t([-g(t),g(t)])>0 \}. We prove that
\bP\{\tau=\infty\}=0 or 1 according as the integral is finite or infinite.Comment: 14 page
A Chaotic Cipher Mmohocc and Its Randomness Evaluation
After a brief introduction to a new chaotic stream cipher Mmohocc which
utilizes the fundamental chaos characteristics of mixing, unpredictability, and
sensitivity to initial conditions, we conducted the randomness statistical
tests against the keystreams generated by the cipher. Two batteries of most
stringent randomness tests, namely the NIST Suite and the Diehard Suite, were
performed. The results showed that the keystreams have successfully passed all
the statistical tests. We conclude that Mmohocc can generate high-quality
pseudorandom numbers from a statistical point of view.Comment: 8 pages, 4 figures, and 3 tables, submitted to ICCS0
A Chaotic Cipher Mmohocc and Its Security Analysis
In this paper we introduce a new chaotic stream cipher Mmohocc which utilizes
the fundamental chaos characteristics. The designs of the major components of
the cipher are given. Its cryptographic properties of period, auto- and
cross-correlations, and the mixture of Markov processes and spatiotemporal
effects are investigated. The cipher is resistant to the related-key-IV
attacks, Time/Memory/Data tradeoff attacks, algebraic attacks, and chosen-text
attacks. The keystreams successfully passed two batteries of statistical tests
and the encryption speed is comparable with RC4.Comment: 14 pages, 4 figures, 4 table
A distribution-function-valued SPDE and its applications
In this paper we further study the stochastic partial differential equation
first proposed by Xiong (2013). Under localized conditions on the coefficients
we show that the solution is in fact distribution-function-valued and we
establish the pathwise uniqueness of the solution. As applications we obtain
the well-posedness of the martingale problems for two classes of measure-valued
diffusions: interacting super-Brownian motions and interacting Fleming-Viot
processes. Properties of the two superprocesses such as the existence of
density fields and the extinction behaviors are also studied
MG-WFBP: Efficient Data Communication for Distributed Synchronous SGD Algorithms
Distributed synchronous stochastic gradient descent has been widely used to
train deep neural networks on computer clusters. With the increase of
computational power, network communications have become one limiting factor on
system scalability. In this paper, we observe that many deep neural networks
have a large number of layers with only a small amount of data to be
communicated. Based on the fact that merging some short communication tasks
into a single one may reduce the overall communication time, we formulate an
optimization problem to minimize the training iteration time. We develop an
optimal solution named merged-gradient WFBP (MG-WFBP) and implement it in our
open-source deep learning platform B-Caffe. Our experimental results on an
8-node GPU cluster with 10GbE interconnect and trace-based simulation results
on a 64-node cluster both show that the MG-WFBP algorithm can achieve much
better scaling efficiency than existing methods WFBP and SyncEASGD.Comment: 9 pages, INFOCOM 201
How long does the surplus stay close to its historical high?
In this paper we find the Laplace transforms of the weighted occupation times
for a spectrally negative L\'evy surplus process to spend below its running
maximum up to the first exit times. The results are expressed in terms of
generalized scale functions. For step weight functions, the Laplace transforms
can be further expressed in terms of scale functions.Comment: 19page
Branching Particle Systems in Spectrally One-sided Levy Processes
We investigate the branching structure coded by the excursion above zero of a
spectrally positive Levy process. The main idea is to identify the level of the
Levy excursion as the time and count the number of jumps upcrossing the level.
By regarding the size of a jump as the birth site of a particle, we construct a
branching particle system in which the particles undergo nonlocal branchings
and deterministic spatial motions to the left on the positive half line. A
particle is removed from the system as soon as it reaches the origin. Then a
measure-valued Borel right Markov process can be defined as the counting
measures of the particle system. Its total mass evolves according to a
Crump-Mode-Jagers branching process and its support represents the residual
life times of those existing particles. A similar result for spectrally
negative Levy process is established by a time reversal approach. Properties of
the measure-valued processes can be studied via the excursions for the
corresponding Levy processes.Comment: 23pages, 2 figure
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