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In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and dominates, and determine criteria to characterise this…

Classical Analysis and ODEs · Mathematics 2013-10-10 John A. D. Appleby , Michael J. McCarthy , Alexandra Rodkina

We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…

General Economics · Economics 2024-04-12 José Moran , Massimo Riccaboni

The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their…

Economics · Quantitative Finance 2019-04-04 Valentina V. Tarasova , Vasily E. Tarasov

In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…

Group Theory · Mathematics 2016-05-13 Kasra Rafi , Jing Tao

With negative growth in real production in many countries and debt levels which become an increasing burden on developed societies, the calls for a change in economic policy and even the monetary system become louder and increasingly…

General Finance · Quantitative Finance 2012-06-08 Andreas Hula

Most models that try to explain economic growth indicate exponential growth paths. In recent years, however, a lively discussion has emerged considering the validity of this notion. In the empirical literature dealing with drivers of…

Economics · Quantitative Finance 2018-03-06 Steffen Lange , Peter Pütz , Thomas Kopp

In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle.…

Analysis of PDEs · Mathematics 2025-09-03 Prasanta K. Barik , Fernando P. da Costa , João T. Pinto , Rafael Sasportes

The rate equation for an arbitrary mth order growth or decay reaction can be expressed in terms of the q-exponential function, with q equal to m. The analysis suggests that a wide variety of reaction rate (kinetic) processes and models, in…

Statistical Mechanics · Physics 2007-05-23 Robert K. Niven

We establish the existence of a deterministic exponential growth rate for the norm (on an appropriate function space) of the solution of the linear scalar stochastic delay equation dX(t) = X(t-1) dW(t) which does not depend on the initial…

Probability · Mathematics 2012-01-13 Michael Scheutzow

Compound interest as well as inflation grows exponentially with time, whereas other means to repay debt grow polynomially. For this and other, mostly political, reasons, debt without inflation is unsustainable. We suggest a discontinuous…

General Finance · Quantitative Finance 2015-07-13 Karl Svozil

We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly…

Optimization and Control · Mathematics 2019-01-29 Giorgia Callegaro , Claudia Ceci , Giorgio Ferrari

Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete…

Economics · Quantitative Finance 2017-07-25 Valentina V. Tarasova , Vasily E. Tarasov

Monetary inflation is a sustained increase in the money supply than can result in price inflation, which is a rise in the general level of prices of goods and services. The objectives of this paper were to develop economic models to (1)…

General Finance · Quantitative Finance 2021-09-28 Laurence Francis Lacey

Following findings by Ormerod and Mounfield, Wright rises the problem whether a power or an exponential law describes the distribution of occurrences of economic recession periods. In order to clarify the controversy a different set of GDP…

Statistical Mechanics · Physics 2009-11-10 Marcel Ausloos , Janusz Miskiewicz , Michele Sanglier

We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…

General Finance · Quantitative Finance 2018-07-05 Victor E. Gluzberg , Yuri A. Katz

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…

Atmospheric and Oceanic Physics · Physics 2012-11-14 Timothy J. Garrett

In dynamical framework the conflict between government and the central bank according to the exchange Rate of payment of fixed rates and fixed rates of fixed income (EMU) convergence criteria such that the public debt / GDP ratio The method…

Econometrics · Economics 2018-07-24 William Mackenzie

A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…

Economics · Quantitative Finance 2017-01-11 Valentina V. Tarasova , Vasily E. Tarasov

Growth rate of real GDP per capita, GDPpc, is represented as a sum of two components, a monotonically decreasing economic trend and fluctuations related to population change. The economic trend is modelled by an inverse function of GDPpc…

General Economics · Economics 2021-03-23 Ivan Kitov

Exponential growth occurs when the growth rate of a given quantity is proportional to the quantity's current value. Surprisingly, when exponential growth data is plotted as a simple histogram disregarding the time dimension, a remarkable…

Statistics Theory · Mathematics 2019-01-08 Alex Ely Kossovsky
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