Finite-size corrections to Poisson approximations of rare events in renewal processes

Consider a renewal process. The renewal events partition the process into i.i.d. renewal cycles. Assume that on each cycle, a rare event called 'success’ can occur. Such successes lend themselves naturally to approximation by Poisson point processes. If each success occurs after a random delay, however, Poisson convergence may be relatively slow, because each success corresponds to a time interval, not a point. In 1996, Altschul and Gish proposed a finite-size correction to a particular approximation by a Poisson point process. Their correction is now used routinely (about once a second) when computers compare biological sequences, although it lacks a mathematical foundation. This paper generalizes their correction. For a single renewal process or several renewal processes operating in parallel, this paper gives an asymptotic expansion that contains in successive terms a Poisson point approximation, a generalization of the Altschul-Gish correction, and a correction term beyond that.

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Finite size effects in classical string solutions of the Schrödinger geometry

Journal of High Energy Physics ◽

10.1007/jhep08(2020)091 ◽

2020 ◽

Vol 2020 (8) ◽

Cited By ~ 1

Author(s):

Dimitrios Zoakos

Keyword(s):

Size Effects ◽

Correction Term ◽

Finite Size ◽

Dispersion Relations ◽

Leading Order ◽

Finite Size Effects ◽

Single Spin ◽

Single Spike ◽

Size Dispersion ◽

Finite Size Corrections

Abstract We study finite size corrections to the semiclassical string solutions of the Schrödinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a S3 subspace of the five-sphere and extent in the Schrödinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed AdS5 × S5 counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.

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FINITE SIZE CORRECTIONS FOR MULTIPARTICLE SPIN-½ NONLINEAR SCHRÖDINGER MODEL

Modern Physics Letters B ◽

10.1142/s021798499100191x ◽

1991 ◽

Vol 05 (23) ◽

pp. 1603-1606

Author(s):

YI-MIN LIU ◽

FU-CHO PU ◽

HANG SU

Keyword(s):

Critical Point ◽

Ground State ◽

Finite Size ◽

Conformal Anomaly ◽

Nonlinear Schrödinger ◽

Size Correction ◽

Finite Size Correction ◽

Finite Size Corrections ◽

Maclaurin Formula

Applied Euler-Maclaurin formula, we compute the finite size correction to the energy of the ground state for the Spin-½ Nonlinear Schrödinger model. We get conformal anomaly for this model at the critical point (T=0).

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Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes

Journal of Applied Probability ◽

10.1017/s002190020010806x ◽

1985 ◽

Vol 22 (04) ◽

pp. 828-835 ◽

Cited By ~ 2

Author(s):

J. Chandramohan ◽

Lung-Kuang Liang

Keyword(s):

Markov Chain ◽

Poisson Process ◽

Renewal Process ◽

Point Processes ◽

Renewal Processes ◽

Single Pair ◽

Doubly Stochastic ◽

Doubly Stochastic Poisson Process ◽

Non Homogeneous Poisson Process ◽

Dependent Point

We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

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FINITE SIZE CORRECTION ON THE SURFACE WIDTH OF RANDOM DEPOSITION WITH SURFACE RELAXATION MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979206035370 ◽

2006 ◽

Vol 20 (21) ◽

pp. 3057-3070

Author(s):

A. A. MASOUDI ◽

R. ZARGINI

Keyword(s):

Fourier Transformation ◽

Finite Size ◽

Surface Relaxation ◽

Nonlinear Coupling ◽

Relaxation Model ◽

Coupling Constant ◽

The Mean ◽

Size Correction ◽

Finite Size Correction ◽

Finite Size Corrections

The Kardar–Parizi–Zhang equation for surface growth has been analyzed in the regime where the nonlinear coupling constant, λ, is small (Edwards–Wilkinson equation). By using the Fourier transformation the finite size corrections on the mean-square width could be calculated. It is found that the calculated interface width for [Formula: see text] behaves as [Formula: see text] and for [Formula: see text] behaves like [Formula: see text].

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Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes

Journal of Applied Probability ◽

10.2307/3213950 ◽

1985 ◽

Vol 22 (4) ◽

pp. 828-835 ◽

Cited By ~ 6

Author(s):

J. Chandramohan ◽

Lung-Kuang Liang

Keyword(s):

Markov Chain ◽

Poisson Process ◽

Renewal Process ◽

Point Processes ◽

Renewal Processes ◽

Single Pair ◽

Doubly Stochastic ◽

Doubly Stochastic Poisson Process ◽

Non Homogeneous Poisson Process ◽

Dependent Point

We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

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The square-wave spectral density of a stationary renewal process

Journal of Applied Mathematics and Simulation ◽

10.1155/s1048953389000109 ◽

1989 ◽

Vol 2 (2) ◽

pp. 117-130 ◽

Cited By ~ 2

Author(s):

Marcel F. Neuts ◽

H. Sitaraman

Keyword(s):

Qualitative Study ◽

Spectral Density ◽

Renewal Process ◽

Stationary Point ◽

Point Processes ◽

Renewal Processes ◽

Square Wave ◽

Promising Tool ◽

Power Spectral ◽

Stationary Point Processes

The power spectral density of a random square wave is a promising tool in the qualitative study of stationary point processes. This is illustrated for renewal processes and their superpositions.

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Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽

10.3390/math9010055 ◽

2020 ◽

Vol 9 (1) ◽

pp. 55

Author(s):

P.-C.G. Vassiliou

Keyword(s):

Markov Chain ◽

Probability Measure ◽

Renewal Process ◽

Markov Chain Model ◽

Markov Renewal Process ◽

Renewal Processes ◽

Chain Model ◽

Markov Renewal Processes ◽

Risky Bonds ◽

Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

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Geometrically confined thermal field theory: Finite size corrections and phase transitions

Physical Review D ◽

10.1103/physrevd.102.116017 ◽

2020 ◽

Vol 102 (11) ◽

Author(s):

Sylvain Mogliacci ◽

Isobel Kolbé ◽

W. A. Horowitz

Keyword(s):

Field Theory ◽

Phase Transitions ◽

Thermal Field Theory ◽

Thermal Field ◽

Finite Size ◽

Finite Size Corrections ◽

Geometrically Confined

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NUMERICAL STUDY OF CHARGE AND STATISTICS OF LAUGHLIN QUASIPARTICLES

International Journal of Modern Physics A ◽

10.1142/s0217751x99000270 ◽

1999 ◽

Vol 14 (04) ◽

pp. 537-557 ◽

Cited By ~ 31

Author(s):

HEIDI KJØNSBERG ◽

JAN MYRHEIM

Keyword(s):

Numerical Study ◽

Finite Size ◽

Expected Value ◽

Wave Functions ◽

Numerical Calculations ◽

Filling Fraction ◽

Slow Convergence ◽

Berry Phases ◽

Size Correction ◽

Finite Size Correction

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasiparticles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasiholes our results confirm that the charge and statistics parameter are e/3 and 1/3, respectively. For the quasielectron charge we find a slow convergence towards the expected value of -e/3, with a finite size correction for N electrons of approximately -0.13e/N. The statistics parameter for the quasielectrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. The anyon model works well for the quasiholes, but requires singular two-anyon wave functions for modelling two Laughlin quasielectrons.

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