A Criterion of Convergence of Generalized Processes and an Application to a Supercritical Branching Particle System

1991 ◽  
Vol 43 (5) ◽  
pp. 985-997 ◽  
Author(s):  
Begoña Fernández ◽  
Luis G. Gorostiza
Keyword(s):  
Particle System ◽  
Continuous Process ◽  
Integral Functional ◽  
Convergence Criterion ◽  
Convergence In Distribution ◽  
Branching Particle System ◽  
Recent Theorem ◽  
A Minor ◽  
Generalized Processes ◽  
Special Case

The problem of convergence in distribution of a large class of generalized semimartingales to a continuous process is considerably simplified by a recent theorem of Aldous [1], in conjunction with a result of Cremers and Kadelka [3] on convergence of integral functional, and the results of Mitoma [15] and Fouque [8] for generalized processes. We will give a convenient convergence criterion in this setting. The proof amounts to a direct combination of the results of the abovementioned authors, requiring only a minor extension (of a special case) of the theorem of Cremers and Kadelka.

Immigration processes associated with branching particle systems

1998 ◽  
Vol 30 (03) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Particle System ◽  
Random Measure ◽  
Particle Systems ◽  
Poisson Random Measure ◽  
General Representation ◽  
Branching Particle System ◽  
Convolution Semigroups ◽  
Entrance Law ◽  
Skew Convolution Semigroup ◽  
Special Case

The immigration processes associated with a given branching particle system are formulated by skew convolution semigroups. It is shown that every skew convolution semigroup corresponds uniquely to a locally integrable entrance law for the branching particle system. The immigration particle system may be constructed using a Poisson random measure based on a Markovian measure determined by the entrance law. In the special case where the underlying process is a minimal Brownian motion in a bounded domain, a general representation is given for locally integrable entrance laws for the branching particle system. The convergence of immigration particle systems to measure-valued immigration processes is also studied.

Immigration processes associated with branching particle systems

1998 ◽  
Vol 30 (3) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Particle System ◽  
Random Measure ◽  
Particle Systems ◽  
Poisson Random Measure ◽  
General Representation ◽  
Branching Particle System ◽  
Convolution Semigroups ◽  
Entrance Law ◽  
Skew Convolution Semigroup ◽  
Special Case

The immigration processes associated with a given branching particle system are formulated by skew convolution semigroups. It is shown that every skew convolution semigroup corresponds uniquely to a locally integrable entrance law for the branching particle system. The immigration particle system may be constructed using a Poisson random measure based on a Markovian measure determined by the entrance law. In the special case where the underlying process is a minimal Brownian motion in a bounded domain, a general representation is given for locally integrable entrance laws for the branching particle system. The convergence of immigration particle systems to measure-valued immigration processes is also studied.

scholarly journals A large deviation principle for a Brownian immigration particle system

2005 ◽  
Vol 42 (04) ◽  
pp. 1120-1133
Author(s):  
Mei Zhang
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Particle System ◽  
Random Measure ◽  
Poisson Random Measure ◽  
Intensity Measure ◽  
Branching Particle System ◽  
Deviation Principle

We derive a large deviation principle for a Brownian immigration branching particle system, where the immigration is governed by a Poisson random measure with a Lebesgue intensity measure.

scholarly journals Diversification events and the effects of mass extinctions on Crocodyliformes evolutionary history

2015 ◽  
Vol 2 (5) ◽  
pp. 140385 ◽  
Author(s):  
Mario Bronzati ◽  
Felipe C. Montefeltro ◽  
Max C. Langer
Keyword(s):  
Mass Extinction ◽  
Fossil Record ◽  
Evolutionary History ◽  
Continuous Process ◽  
Mass Extinctions ◽  
Terrestrial Habitats ◽  
History Of ◽  
The Rich ◽  
A Minor ◽  
Diversification Event

The rich fossil record of Crocodyliformes shows a much greater diversity in the past than today in terms of morphological disparity and occupation of niches. We conducted topology-based analyses seeking diversification shifts along the evolutionary history of the group. Our results support previous studies, indicating an initial radiation of the group following the Triassic/Jurassic mass extinction, here assumed to be related to the diversification of terrestrial protosuchians, marine thalattosuchians and semi-aquatic lineages within Neosuchia. During the Cretaceous, notosuchians embodied a second diversification event in terrestrial habitats and eusuchian lineages started diversifying before the end of the Mesozoic. Our results also support previous arguments for a minor impact of the Cretaceous/Palaeogene mass extinction on the evolutionary history of the group. This argument is not only based on the information from the fossil record, which shows basal groups surviving the mass extinction and the decline of other Mesozoic lineages before the event, but also by the diversification event encompassing only the alligatoroids in the earliest period after the extinction. Our results also indicate that, instead of a continuous process through time, Crocodyliformes diversification was patchy, with events restricted to specific subgroups in particular environments and time intervals.

A probabilistic proof of non-explosion of a non-linear PDE system

2000 ◽  
Vol 37 (03) ◽  
pp. 635-641 ◽  
Author(s):  
J. Alfredo López-Mimbela ◽  
Anton Wakolbinger
Keyword(s):  
Positive Solutions ◽  
Initial Conditions ◽  
Particle System ◽  
Stable Processes ◽  
Symmetric Stable Processes ◽  
Branching Particle System ◽  
Independent Increments ◽  
Non Linear ◽  
Probabilistic Proof ◽  
Processes With Independent Increments

Using a representation in terms of a two-type branching particle system, we prove that positive solutions of the system remain bounded for suitable bounded initial conditions, provided A and B generate processes with independent increments and one of the processes is transient with a uniform power decay of its semigroup. For the case of symmetric stable processes on R 1,this answers a question raised in [4].

scholarly journals OCCUPATION TIME FLUCTUATION LIMITS OF INFINITE VARIANCE EQUILIBRIUM BRANCHING SYSTEMS

2009 ◽  
Vol 12 (04) ◽  
pp. 593-612 ◽  
Author(s):  
PIOTR MIŁOŚ
Keyword(s):  
Particle System ◽  
Random Measure ◽  
Domain Of Attraction ◽  
Interesting Case ◽  
Occupation Time ◽  
Infinite Variance ◽  
Dependence Structure ◽  
Branching Particle System ◽  
Stable Motion ◽  
Fractional Stable Motion

We establish limit theorems for the fluctuations of the rescaled occupation time of a (d, α, β)-branching particle system. It consists of particles moving according to a symmetric α-stable motion in ℝd. The branching law is in the domain of attraction of a (1 + β)-stable law and the initial condition is the equilibrium random measure for the system (defined below). In the paper we treat separately the cases of intermediate α/β < d < (1 + β)α/β, critical d = (1 + β)α/β and large d > (1 + β)α/β dimensions. In the most interesting case of intermediate dimensions we obtain a version of a fractional stable motion. The long-range dependence structure of this process is also studied. Contrary to this case, limit processes in critical and large dimensions have independent increments.

scholarly journals Understanding the concept of Purgation (Ishal) in Unani Medicine: A Review

2021 ◽  
Vol 11 (2) ◽  
pp. 241-246
Author(s):  
Hina V Kouser ◽  
Fatima Khan ◽  
Ayesha Tehseen ◽  
Mohd Nayab ◽  
Abdul Nasir Ansari
Keyword(s):  
Chronic Diseases ◽  
Continuous Process ◽  
The Body ◽  
Main Determinant ◽  
Unani Medicine ◽  
Disease Elimination ◽  
Concept Of Health ◽  
Health And Disease ◽  
A Minor

The theory of humours (akhlat) is one of the fundamental pillars of the Unani System of Medicine (USM). The concept of health and disease depends on the quality (kaifiyat) and quantity (kammiyat) of humour (khilt). Health (sehat) lasts when humours remain in equilibrium and the main determinant of health is the balance in six essential factors (asbab-e-sittah zarooriya). These factors are highly modifiable and deviation in any of them leads to disequilibrium in humours either qualitatively or quantitatively which ultimately manifests in the form of the disease. Elimination (istifragh) of these morbid humours from the body becomes mandatory to treat the diseases or to restore health. One of the effective methods of elimination is purgation (ishal). It is a method by which morbid humours from the body are eliminated through the anal route. Before the elimination of any pathological humour especially in chronic diseases, it is mandatory to make the humour easily eliminable. This process of making the pathological humour eliminable is known as concoction (nuzj). The process of concoction is a regular and continuous process of the tabiyat (mediatrix naturae) of the body. In case of a minor deviation in humour, tabiyat itself eliminates it from the body after concoction. When the causative pathological humours are in abundance or grossly deviated from normalcy, tabiyat needs help from outside the body. This help of tabiyat can be done with some humour specific drugs which are known as concoctive medicines (munzij advia). Once, the humours become eliminable, the process of evacuation can be started. Classical Unani literature and published papers were explored to find the rationale of purgation therapy. Purgation is found to be advisable in the treatment of many chronic diseases. Tabiyat is the ultimate healer in the body and purgation helps it to overcome the diseases. Keywords: Istifragh; Munzij; Nuzj; Akhlat; Humours; Concoction

scholarly journals Numerical investigation of particle motion at the steel—slag interface in continuous casting using VOF method and dynamic overset grids

2022 ◽  
Author(s):  
Xiaomeng Zhang ◽  
Stefan Pirker ◽  
Mahdi Saeedipour
Keyword(s):  
Particle Motion ◽  
Particle System ◽  
Particle Density ◽  
Steel Slag ◽  
Physical Parameters ◽  
Slag Particle ◽  
Dynamic Overset Grids ◽  
Capillary Interactions ◽  
Speed Up ◽  
A Minor

AbstractThe capillary interactions are prominent for a micro-sized particle at the steel—slag interface. In this study, the dynamics of a spherical particle interacting with the steel—slag interface is numerically investigated using the volume of fluid method in combination with the overset grid technique to account for particle motion. The simulations have shown the particle’s separation process at the interface and successfully captured the formation and continuous evolution of a meniscus in the course of particle motion. A sensitivity analysis on the effect of different physical parameters in the steel—slag—particle system is also conducted. The result indicates that the wettability of particle with the slag phase is the main factor affecting particle separation behavior (trapped at the interface or fully separated into slag). Higher interfacial tension of fluid interface and smaller particle size can speed up the particle motion but have less effect on the equilibrium position for particle staying at the interface. In comparison, particle density shows a minor influence when the motion is dominated by the capillary effect. By taking account of the effect of meniscus and capillary forces on a particle, this study provides a more accurate simulation of particle motion in the vicinity of the steel—slag interface and enables further investigation of more complex situations.

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