scholarly journals Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes

2018 ◽  
Vol 50 (01) ◽  
pp. 74-101 ◽  
Author(s):  
Viktor Bezborodov ◽  
Luca Di Persio ◽  
Tyll Krueger ◽  
Mykola Lebid ◽  
Tomasz Ożański
Keyword(s):  
Continuous Time ◽  
Birth Rate ◽  
Growth Models ◽  
Classical Lattice ◽  
Continuous Space ◽  
Asymptotic Shape ◽  
Subadditive Ergodic Theorem ◽  
Speed Of Propagation ◽  
Birth Processes ◽  
Precise Expression

AbstractWe formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar to the classical lattice growth models, the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free-branching birth rate.

scholarly journals Corrigendum to: Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes

2020 ◽  
Vol 52 (4) ◽  
pp. 1325-1327
Author(s):  
V. Bezborodov
Keyword(s):  
Continuous Time ◽  
Continuous Space ◽  
Asymptotic Shape ◽  
Speed Of Propagation ◽  
Birth Processes

AbstractWe would like to correct the statement of Lemma 4.1 in [BDK+18].

scholarly journals Existence of solutions in continuous-time optimal growth models

2008 ◽  
Vol 37 (2) ◽  
pp. 321-333 ◽  
Author(s):  
Hippolyte d’Albis ◽  
Pascal Gourdel ◽  
Cuong Le Van
Keyword(s):  
Continuous Time ◽  
Existence Of Solutions ◽  
Growth Models ◽  
Optimal Growth ◽  
Time Optimal ◽  
Optimal Growth Models

Exponential ergodicity for single-birth processes

2004 ◽  
Vol 41 (4) ◽  
pp. 1022-1032 ◽  
Author(s):  
Yong-Hua Mao ◽  
Yu-Hui Zhang
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
New Method ◽  
Sufficient Condition ◽  
Exponential Ergodicity ◽  
Comparison Methods ◽  
Birth Processes ◽  
Single Birth ◽  
Continuous Time Branching Processes

An explicit, computable, and sufficient condition for exponential ergodicity of single-birth processes is presented. The corresponding criterion for birth–death processes is proved using a new method. As an application, some sufficient conditions are obtained for exponential ergodicity of an extended class of continuous-time branching processes and of multidimensional Q-processes, by comparison methods.

Non-existence of optimal programs for undiscounted growth models in continuous time

2017 ◽  
Vol 152 ◽  
pp. 57-61
Author(s):  
Giorgio Fabbri ◽  
Silvia Faggian ◽  
Giuseppe Freni
Keyword(s):  
Continuous Time ◽  
Growth Models ◽  
Existence Of Optimal Programs

Infinite-horizon continuous-time growth models

1996 ◽  
Vol 27 (4) ◽  
pp. 373-378
Author(s):  
DIMITRIOS KRAVVARITIS ◽  
NIKOLAOS S. PAPAGEORGIOU
Keyword(s):  
Continuous Time ◽  
Growth Models ◽  
Infinite Horizon

On the identification of continuous-time Markov chains with a given invariant measure

1994 ◽  
Vol 31 (04) ◽  
pp. 897-910
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Continuous Time ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Birth Process ◽  
Continuous Time Markov Chains ◽  
Branching Process With Immigration ◽  
Birth Processes ◽  
Necessary And Sufficient

In [14] a necessary and sufficient condition was obtained for there to exist uniquely a Q-process with a specified invariant measure, under the assumption that Q is a stable, conservative, single-exit matrix. The purpose of this note is to demonstrate that, for an arbitrary stable and conservative q-matrix, the same condition suffices for the existence of a suitable Q-process, but that this process might not be unique. A range of examples is considered, including pure-birth processes, a birth process with catastrophes, birth-death processes and the Markov branching process with immigration.

Strong ergodicity for single-birth processes

2001 ◽  
Vol 38 (01) ◽  
pp. 270-277 ◽  
Author(s):  
Yu-Hui Zhang
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Strong Ergodicity ◽  
Finite Dimensional ◽  
Comparison Methods ◽  
Schlögl Model ◽  
Birth Processes ◽  
Single Birth ◽  
Continuous Time Branching Processes

An explicit and computable criterion for strong ergodicity of single-birth processes is presented. As an application, some sufficient conditions are obtained for strong ergodicity of an extended class of continuous-time branching processes and multi-dimensional Q-processes by comparison methods respectively. Consequently strong ergodicity of the Q-process corresponding to the finite-dimensional Schlögl model is proven.

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