On supercritical Galton-Watson processes allowing immigration

1974 ◽  
Vol 11 (4) ◽  
pp. 814-817 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Absolute Continuity ◽  
Branching Processes ◽  
Random Variables ◽  
The Other ◽  
State Dependent ◽  
The Absolute

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

On supercritical Galton-Watson processes allowing immigration

1974 ◽  
Vol 11 (04) ◽  
pp. 814-817 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Absolute Continuity ◽  
Branching Processes ◽  
Random Variables ◽  
The Other ◽  
State Dependent ◽  
The Absolute

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (4) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval.In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes

1975 ◽  
Vol 7 (01) ◽  
pp. 66-82 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Continuous State Space ◽  
Continuous State ◽  
Integer Exponent

We obtain results connecting the distribution of the random variablesYandWin the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1,EYβandEWβconverge or diverge together and regular variation of the tail of one ofY, Wwith non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes

1975 ◽  
Vol 7 (1) ◽  
pp. 66-82 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Continuous State Space ◽  
Continuous State ◽  
Integer Exponent

We obtain results connecting the distribution of the random variables Y and W in the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1, EYβ and EWβ converge or diverge together and regular variation of the tail of one of Y, W with non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

scholarly journals A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1505
Author(s):  
Evgeniy Anatolievich Savinov
Keyword(s):  
Absolute Continuity ◽  
Joint Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Necessary Condition ◽  
Conditional Distributions ◽  
One Dimensional ◽  
The Absolute

Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n>1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.

Asymptotic properties of supercritical branching processes I: The Galton-Watson process

1974 ◽  
Vol 6 (4) ◽  
pp. 711-731 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Integer Exponent ◽  
Watson Process ◽  
Supercritical Branching Processes

We obtain results connecting the distributions of the random variables Z1 and W in the supercritical Galton-Watson process. For example, if a > 1, and converge or diverge together, and regular variation of the tail of one of Z1, W with non-integer exponent α > 1 is equivalent to regular variation of the tail of the other.

Asymptotic properties of supercritical branching processes I: The Galton-Watson process

1974 ◽  
Vol 6 (04) ◽  
pp. 711-731 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Integer Exponent ◽  
Watson Process ◽  
Supercritical Branching Processes

We obtain results connecting the distributions of the random variables Z 1 and W in the supercritical Galton-Watson process. For example, if a > 1, and converge or diverge together, and regular variation of the tail of one of Z 1, W with non-integer exponent α > 1 is equivalent to regular variation of the tail of the other.

On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (04) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval. In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

The World after the End of the World

2017 ◽  
Vol 39 (2) ◽  
pp. 265-276 ◽  
Author(s):  
Kas Saghafi
Keyword(s):  
The Other ◽  
The World ◽  
History Of ◽  
The Absolute ◽  
End Of The World

In several late texts, Derrida meditated on Paul Celan's poem ‘Grosse, Glühende Wölbung’, in which the departure of the world is announced. Delving into the ‘origin’ and ‘history’ of the ‘conception’ of the world, this paper suggests that, for Derrida, the end of the world is determined by and from death—the death of the other. The death of the other marks, each and every time, the absolute end of the world.

Moderne Ikonen

2009 ◽  
Vol 54 (2) ◽  
pp. 123-143
Author(s):  
Bernadette Collenberg-Plotnikov
Keyword(s):  
Mass Culture ◽  
Visual Experience ◽  
Modern Art ◽  
The Other ◽  
Recent Discussion ◽  
Christian Church ◽  
Other Hand ◽  
The Absolute ◽  
Modern Mass

›Ikonen‹ sind heute nicht mehr nur die Ikonen der christlichen Kirche, sondern vor allem die Ikonen der modernen Massenkultur. Beide Arten von Ikonen werden in der neueren Kunstreflexion aufgegriffen: Kunst gilt entweder, verstanden als Erbin der religiösen Ikone, als Phänomen, das Absolutes in singulärer Weise anschaulich er- fahrbar macht. Oder aber die Kunst gilt umgekehrt lediglich als Klasse in der Welt der säkularen Ikonen. Demgegenüber wird im Beitrag erstens die These vertretenwerden, daß die neuere Kunst sowohl Aspekte transzendenter als auch immanenter Ikonen umfaßt. Zugleich ist es aber, so die zweite These, für unser Kunstverständnis charakteristisch, ein theoretisches Kontrastverhältnis zwischen Kunst und Ikone an- zunehmen. Dieses gründet auf einer spezifischen Reflexivität der Kunst, durch die sie sich von der Ikone beiderlei Art kategorial unterscheidet. Today, the word ›icon‹ usually no longer refers to the icons of the Christian church, but to the icons of the modern mass-culture. Both sorts of icons play a key-role in the recent discussion about art: Either art is supposed to be a descendant of the religious icon, a phenomenon that gives us a singular visual experience of the Absolute. On the other hand, art is supposed to be just one class among others in the wide world of the secular icons. In contrast to these two positions this essay contends that modern art comprehends aspects of transcendent as well as of immanent icons. Furthermore, it argues that at the same time it is characteristic for our notion of art to suppose a contrast between art and icon. This contrast is based on a specific reflectivity of art, which marks a categorical difference between art and both sorts of icons.

Sign in / Sign up

Export Citation Format

Share Document