scholarly journals On the genealogy of branching populations and their diffusion limits

2018 ◽  
Vol 50 (A) ◽  
pp. 173-176
Author(s):  
Olav Kallenberg
Keyword(s):  
Branching Process ◽  
Diffusion Limit ◽  
The Past ◽  
Diffusion Limits

Abstract We consider the evolution of the ancestral structure of a classical branching process in space and its diffusion limit. We also indicate how the conditional structure of the past can be described asymptotically in terms of suitable uniform Brownian trees.

Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits

2016 ◽  
Vol 53 (2) ◽  
pp. 410-420 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Weak Limit ◽  
Diffusion Limit ◽  
Complexity Bounds ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Diffusion Limits ◽  
Random Walk Metropolis Algorithm

Abstract We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the computer science notion of algorithm complexity. Our main result states that any weak limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate assumptions, the random-walk Metropolis algorithm in d dimensions takes O(d) iterations to converge to stationarity, while the Metropolis-adjusted Langevin algorithm takes O(d1/3) iterations to converge to stationarity.

scholarly journals WEAK DIFFUSION LIMITS OF DYNAMIC CONDITIONAL CORRELATION MODELS

2016 ◽  
Vol 33 (3) ◽  
pp. 691-716 ◽  
Author(s):  
Christian M. Hafner ◽  
Sebastien Laurent ◽  
Francesco Violante
Keyword(s):  
Monte Carlo Experiment ◽  
Diffusion Limit ◽  
Conditional Correlation ◽  
Dynamic Conditional Correlation ◽  
Reduced Rank ◽  
Correlation Models ◽  
Diffusion Parameters ◽  
Diffusion Limits ◽  
Special Case ◽  
Weak Diffusion

The properties of dynamic conditional correlation (DCC) models, introduced more than a decade ago, are still not entirely known. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a nondegenerate diffusion limit can be obtained. Alternative sets of conditions are considered for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the often used quasi-approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may provide reasonable approximations for sufficiently large frequencies and sample sizes.

A limit theorem for the maxima of the para-critical simple branching process

1998 ◽  
Vol 30 (3) ◽  
pp. 740-756 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Limit Theorem ◽  
Branching Process ◽  
Branching Processes ◽  
Weak Limit ◽  
Hitting Time ◽  
Functional Limit Theorem ◽  
Diffusion Limit ◽  
Bessel Processes ◽  
Functional Limit ◽  
The Law

Let Mn denote the size of the largest amongst the first n generations of a simple branching process. It is shown for near critical processes with a finite offspring variance that the law of Mn/n, conditioned on no extinction at or before n, has a non-defective weak limit. The proof uses a conditioned functional limit theorem deriving from the Feller-Lindvall (CB) diffusion limit for branching processes descended from increasing numbers of ancestors. Subsidiary results are given about hitting time laws for CB diffusions and Bessel processes.

A limit theorem for the maxima of the para-critical simple branching process

1998 ◽  
Vol 30 (03) ◽  
pp. 740-756 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Limit Theorem ◽  
Branching Process ◽  
Branching Processes ◽  
Weak Limit ◽  
Hitting Time ◽  
Functional Limit Theorem ◽  
Diffusion Limit ◽  
Bessel Processes ◽  
Functional Limit ◽  
The Law

Let M n denote the size of the largest amongst the first n generations of a simple branching process. It is shown for near critical processes with a finite offspring variance that the law of M n /n, conditioned on no extinction at or before n, has a non-defective weak limit. The proof uses a conditioned functional limit theorem deriving from the Feller-Lindvall (CB) diffusion limit for branching processes descended from increasing numbers of ancestors. Subsidiary results are given about hitting time laws for CB diffusions and Bessel processes.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

Observations of the continuum near the galactic centre

1967 ◽  
Vol 31 ◽  
pp. 405
Author(s):  
F. J. Kerr
Keyword(s):  
Galactic Centre ◽  
The Past ◽  
Centre Region ◽  
The Continuum

A continuum survey of the galactic-centre region has been carried out at Parkes at 20 cm wavelength over the areal11= 355° to 5°,b11= -3° to +3° (Kerr and Sinclair 1966, 1967). This is a larger region than has been covered in such surveys in the past. The observations were done as declination scans.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

On The Possibility of an Autonomous History of Modern Southeast Asia

1961 ◽  
Vol 2 (2) ◽  
pp. 73-105 ◽  
Author(s):  
John R. W. Small
Keyword(s):  
Southeast Asia ◽  
Contemporary History ◽  
The Past ◽  
History Of

It is generally accepted that history is an element of culture and the historian a member of society, thus, in Croce's aphorism, that the only true history is contemporary history. It follows from this that when there occur great changes in the contemporary scene, there must also be great changes in historiography, that the vision not merely of the present but also of the past must change.

Stellar Evolution

1962 ◽  
Vol 11 (02) ◽  
pp. 137-143
Author(s):  
M. Schwarzschild
Keyword(s):  
Solar System ◽  
Stellar Evolution ◽  
Space Craft ◽  
New Techniques ◽  
Substantial Body ◽  
Individual Stars ◽  
The Past ◽  
Evolution Of Galaxies ◽  
History Of ◽  
Fast Flow

It is perhaps one of the most important characteristics of the past decade in astronomy that the evolution of some major classes of astronomical objects has become accessible to detailed research. The theory of the evolution of individual stars has developed into a substantial body of quantitative investigations. The evolution of galaxies, particularly of our own, has clearly become a subject for serious research. Even the history of the solar system, this close-by intriguing puzzle, may soon make the transition from being a subject of speculation to being a subject of detailed study in view of the fast flow of new data obtained with new techniques, including space-craft.

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