scholarly journals On the Asymptotic Behaviour of Discrete Time Stochastic Growth Processes

1987 ◽  
Vol 15 (1) ◽  
pp. 305-343 ◽  
Author(s):  
G. Keller ◽  
G. Kersting ◽  
U. Rosler
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Growth Processes ◽  
Stochastic Growth

A nonlinear stochastic growth model on discrete time domains

2016 ◽  
Vol 22 (11) ◽  
pp. 1732-1746 ◽  
Author(s):  
Ferhan M. Atıcı ◽  
Gang Cheng ◽  
Alex Lebedinsky
Keyword(s):  
Growth Model ◽  
Discrete Time ◽  
Stochastic Growth ◽  
Stochastic Growth Model ◽  
Time Domains

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

scholarly journals Universal fractality of morphological transitions in stochastic growth processes

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
J. R. Nicolás-Carlock ◽  
J. L. Carrillo-Estrada ◽  
V. Dossetti
Keyword(s):  
Growth Processes ◽  
Stochastic Growth ◽  
Morphological Transitions

scholarly journals Pólya Urns Via the Contraction Method

2014 ◽  
Vol 23 (6) ◽  
pp. 1148-1186 ◽  
Author(s):  
MARGARETE KNAPE ◽  
RALPH NEININGER
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Normal Limit ◽  
Rooted Trees ◽  
Limit Laws ◽  
Contraction Method ◽  
Limit Distributions

We propose an approach to analysing the asymptotic behaviour of Pólya urns based on the contraction method. For this, a new combinatorial discrete-time embedding of the evolution of the urn into random rooted trees is developed. A decomposition of these trees leads to a system of recursive distributional equations which capture the distributions of the numbers of balls of each colour. Ideas from the contraction method are used to study such systems of recursive distributional equations asymptotically. We apply our approach to a couple of concrete Pólya urns that lead to limit laws with normal limit distributions, with non-normal limit distributions and with asymptotic periodic distributional behaviour.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (04) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

scholarly journals Sojourn times in finite Markov processes

1989 ◽  
Vol 26 (4) ◽  
pp. 744-756 ◽  
Author(s):  
Gerardo Rubino ◽  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Sojourn Time ◽  
Sojourn Times ◽  
Finite State ◽  
Sojourn Time Distributions ◽  
Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

Random growth in a tessellation

1973 ◽  
Vol 74 (3) ◽  
pp. 515-528 ◽  
Author(s):  
Daniel Richardson
Keyword(s):  
Euclidean Space ◽  
Growth Process ◽  
Dimensional Euclidean Space ◽  
Growth Processes ◽  
Stochastic Growth ◽  
Random Growth

Let S be n dimensional Euclidean space and let T be a division of S into cells. Assume that each cell must be either white or black at any time t. At time 0 the cell at the origin, α0, is black and all other cells are white. Let G be some stochastic growth process which tends to change white cells with black neighbours into black cells. Let C(t) be the black shape at time t. For a family, F, of such growth processes we prove the following theorem.

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