Stochastic Dynamics of Economic Cycles

Viacheslav Karmalita

• Publisher: De Gruyter
• Year: 2020
• ISBN:
  9783110707038
• Edition: 1
• Topic: Matematica
• Subtopic: Probabilità e statistica

This book includes discussions related to solutions of such tasks as:

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• probabilistic description of the investment function;

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• recovering the income function from GDP estimates;

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• development of models for the economic cycles;

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• selecting the time interval of pseudo-stationarity of cycles;

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• estimating characteristics/parameters of cycle models;

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• analysis of accuracy of model factors.

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All of the above constitute the general principles of a theory explaining the phenomenon of economic cycles and provide mathematical tools for their quantitative description. The introduced theory is applicable to macroeconomic analyses as well as econometric estimations of economic cycles.

Chapter I Elements of Probability Theory

Stochastic approaches presented in this book make it necessary to discuss mathematical models related to the concept of probability. This chapter deals with models that are mathematical descriptions of random phenomena. The following material is devoted to presentation of such models as well as examination of their properties.

1.1 Random Variable

Let us turn to a certain phenomenon whose observation results from a sample space A. Elements (points) of this space may be grouped by different ways into subspaces A₁, …, A_i, …, A_k referred to as events. Appearance of an experimental result inside any subspace implies the occurrence of a specific event. That is to say, the experiment always results in the event:

$\mathbf{A}={\mathrm{A}}_1+{\mathrm{A}}_2+\cdots +{\mathrm{A}}_k.$

A certain event A_i may be given a quantitative characteristic through the frequency of this event’s occurrence in n experiments. Let m(A_i) be the number of experiments in which the event A_i was observed. Then the frequency ν(A_i) of this event (event frequency) can be determined by the follow...