Asymptotic results for non-linear processes of the McKean tagged-molecule type

1986 ◽  
Vol 23 (1) ◽  
pp. 42-51
Author(s):  
Gaston Giroux
Keyword(s):  
Markov Chain ◽  
Branching Processes ◽  
Similar Process ◽  
Homogeneous Markov Chain ◽  
Asymptotic Results ◽  
Linear Processes ◽  
Weak Homogeneity ◽  
Non Linear ◽  
H Theorem ◽  
Molecule Type

McKean's tagged-molecule process is a non-linear homogeneous two-state Markov chain in continuous time, constructed with the aid of a binary branching process. For each of a large class of branching processes we construct a similar process. The construction is carefully done and the weak homogeneity is deduced. A simple probability argument permits us to show convergence to the equidistribution (½, ½) and to note that this limit is a strong equilibrium. A non-homogeneous Markov chain result is also used to establish the geometric rate of convergence. A proof of a Boltzmann H-theorem is also established.

Asymptotic results for non-linear processes of the McKean tagged-molecule type

1986 ◽  
Vol 23 (01) ◽  
pp. 42-51
Author(s):  
Gaston Giroux
Keyword(s):  
Markov Chain ◽  
Branching Processes ◽  
Similar Process ◽  
Homogeneous Markov Chain ◽  
Asymptotic Results ◽  
Linear Processes ◽  
Weak Homogeneity ◽  
Non Linear ◽  
H Theorem ◽  
Molecule Type

McKean's tagged-molecule process is a non-linear homogeneous two-state Markov chain in continuous time, constructed with the aid of a binary branching process. For each of a large class of branching processes we construct a similar process. The construction is carefully done and the weak homogeneity is deduced. A simple probability argument permits us to show convergence to the equidistribution (½, ½) and to note that this limit is a strong equilibrium. A non-homogeneous Markov chain result is also used to establish the geometric rate of convergence. A proof of a Boltzmann H-theorem is also established.

The structure of non-linear processes

Tellus ◽  
1973 ◽  
Vol 25 (6) ◽  
pp. 536-544 ◽  
Author(s):  
A. Quinet
Keyword(s):  
Linear Processes ◽  
Non Linear

Strong ergodicity for continuous-time, non-homogeneous Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 692-694 ◽  
Author(s):  
Mark Scott ◽  
Barry C. Arnold ◽  
Dean L. Isaacson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Homogeneous Markov Chain ◽  
Strong Ergodicity

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

Parametric inference in Markov branching processes with time-dependent random immigration rate

1985 ◽  
Vol 22 (03) ◽  
pp. 503-517
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Processes ◽  
Traditional Approach ◽  
Branching Processes ◽  
External Source ◽  
Time Dependent ◽  
Parametric Inference ◽  
Asymptotic Results ◽  
Subcritical Case ◽  
Immigration Rate ◽  
Pearson Type

The present paper deals with continuous-time Markov branching processes allowing immigration. The immigration rate is allowed to be random and time-dependent where randomness may stem from an external source or from state-dependence. Unlike the traditional approach, we base the analysis of these processes on the theory of multivariate point processes. Using the tools of this theory, asymptotic results on parametric inference are derived for the subcritical case. In particular, the limit distributions of some parametric estimators and of Pearson-type statistics for testing simple and composite hypotheses are established.

scholarly journals Non-central limit theorems for functionals of random fields on hypersurfaces

2020 ◽  
Vol 24 ◽  
pp. 315-340
Author(s):  
Andriy Olenko ◽  
Volodymyr Vaskovych
Keyword(s):  
Rate Of Convergence ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Gaussian Random Fields ◽  
Central Limit Theorems ◽  
Integral Functionals ◽  
Asymptotic Results ◽  
Non Linear ◽  
Linear Integral

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in ℝd. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.

scholarly journals Sustainable Development Goal Drivers in Food Systems

2021 ◽  
Vol 5 ◽  
Author(s):  
Sebastian Kretschmer ◽  
Johannes Kahl
Keyword(s):  
Sustainable Development ◽  
Food Systems ◽  
Sustainable Development Goals ◽  
Food System ◽  
Driving Forces ◽  
Linear Processes ◽  
Non Linear ◽  
Development Goals ◽  
Diagnostic Framework ◽  
Primary Predictor

Interacting driving forces in food systems, resulting in cumulative driver effects and synergies, induce non-linear processes in multiple directions. This paper critically reviews the discourse on driving forces in food systems and argues that mindset is the primary predictor for food system outcomes. In the epoch of sustainable development goals (SDGs) and the Anthropocene, mindset matters more than ever. Transformative narratives are beginning to transcend the dominant social paradigm, which is still driving the food system's overall trajectory. The psychosocial portrayal of the systemic mindset found in organic food systems presented in this paper “flips the script” and hypothesizes that worldview and paradigm have the most causal linkages with unsustainable driver synergies and reversely the biggest leverage on the mitigation thereof. Borrowing from ecological economics discourses, the paper sharpens the driver definition by applying the DPSIR analytical tool as a modified diagnostic framework and modeling approach for food systems. This research sheds new light on the nature of drivers of change, which are often portrayed as almighty and inevitable trends shaping food systems. Instead, it is proposed that drivers emerge from the actors' mindset, affecting food system behavior in a non-linear way. Mindset drives reinforcing feedback loops, resulting in vicious and virtuous cycles. These driver motives manifest in subsystems and continue to drive their interaction across food system elements. Mindset acts as an encapsulated input of food systems, all the while responding to feedback and releasing new drivers. A transformation framework along leverage points of the food system is presented that features the concept of SDG drivers.

scholarly journals The local limit theorem for sums of random variables defined on a homogeneous Markov chain in the case of the stable limit distribution law

1961 ◽  
Vol 1 (1-2) ◽  
pp. 7-16
Author(s):  
A. Aleškevičienė
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Limit Distribution ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Homogeneous Markov Chain ◽  
Stable Limit ◽  
Distribution Law ◽  
Sums Of Random Variables ◽  
Stable Limit Distribution

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: A. Алешкявичене. Локальная предельная теорема для сумм случайных величин, связанных в однородную цепь Маркова в случае устойчивого предельного распределения A. Aleškevičienė. Lokalinė ribinė teorema atsitiktinių dydžių, surištų homogenine Markovo grandine, sumoms stabilaus ribinio dėsnio atveju  

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