The Transition from Brownian Motion to Boom-and-Bust Dynamics in Financial and Economic Systems

With what appears to be the increasing sensitivity of economic/financial systems to various events, whether they be natural disaster, changing financial products or government policy, the need to understand how volatility has changed in modern economic systems and how to recognize when volatility will occur is a topic that is extremely important. This topic has been categorized under various topics such as: business cycles, chaos, dynamic systems, fractals, Brownian motion and super cycles just to name a few. The author believes that all of these areas need to be considered at once when analyzing dynamic phenomena which may have varying degrees of the aforementioned. This chapter will implement a Hicksian Accelerator to develop a framework for stylized facts of general dynamic macroeconomic behavior. The chapter will then implement the model and begin the process of estimating the degree of and sensitivity to volatility in a macro economy.

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RIGIDITIES OF ECONOMIC SYSTEMS AS A FACTOR OF BOOM-AND-BUST ECONOMY

VESTNIK OF VORONEZH STATE AGRARIAN UNIVERSITY ◽

10.17238/issn2071-2243.2019.3.231 ◽

2019 ◽

Vol 3 (62) ◽

pp. 231-237

Author(s):

Olga Yu. Ageeva ◽

◽

Sergey V. Spakhov ◽

Victoria E. Yushkova ◽

◽

...

Keyword(s):

Economic Systems ◽

Boom And Bust

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RIGIDITIES OF ECONOMIC SYSTEMS AS A FACTOR OF BOOM-AND-BUST ECONOMY

VESTNIK OF VORONEZH STATE AGRARIAN UNIVERSITY ◽

10.17238/issn2071-2243.2018.3.231 ◽

2018 ◽

Vol 3 (58) ◽

pp. 231-237

Author(s):

Olga Yu. Ageeva ◽

◽

Sergey V. Spakhov ◽

Victoria E. Yushkova ◽

◽

...

Keyword(s):

Economic Systems ◽

Boom And Bust

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

Author(s):

Allan Sly

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

White Noise ◽

Gaussian Process ◽

Discrete Data ◽

Hölder Exponent ◽

Scaling Properties ◽

Multifractional Brownian Motion ◽

Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

Author(s):

Michael L. Wenocur

Keyword(s):

Brownian Motion ◽

Weibull Distribution ◽

Special Function ◽

Function Theory ◽

Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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