Some nonlinear stochastic growth models

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Some Nonlinear Stochastic Growth Models

Stochastic growth models which generalize GaltonWatson branching processes are discussed. The models have an interpretation in population dynamics and economics. The individuals or particles do interact, e.g. if the individuals represent members of a population, allowance is made for sexual reproduction, so that pairs of individuals are needed to produce offspring. The typical form of the resul...

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Stochastic nonlinear dynamics pattern formation and growth models

Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.

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Stochastic Models of Growth∗

In these notes we describe the existing results on the effects of ‘volatility,’ both in technologies and policies, on the long-run growth rate. We start with a brief summary of the empirical research in this area, and we then describe some simple theoretical models that are useful in understanding the empirical results. We end with the description of some recent work based on the theoretical mo...

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Some Nonlinear Time-series Models

Well-known Box-Jenkins Autoregressive integrated moving average (ARIMA) methodology has virtually dominated analysis of time-series data since 1930s. However, it is applicable to only those data that are either stationary or can be made so. Another limitation is that the resultant model is “Linear”. During the last two decades or so, the area of “Nonlinear time-series” is rapidly growing. Here,...

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Nonlinear Growth Models

A fundamental problem in statistics is to develop models based on a sample of observations and drawing inferences using the model so developed. In growth modeling, data are usually collected over time. One characteristic of such data is that the successive observations are dependent. Each observation of the observed data series Yt may be considered as a realization of a stochastic process {Yt},...

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1971

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1971-12732-5