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Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
We present a macroeconomic agent-based model that combines several mechanisms operating at the same timescale, while remaining mathematically tractable. It comprises enterprises and workers who compete in a job market and a commodity goods…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
This paper brings together divergent approaches to time inconsistency from macroeconomic policy and behavioural economics. Behavioural discount functions from behavioural microeconomics are embedded into a game-theoretic analysis of…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We propose a simple model that describes the dynamics of efficiencies of competing agents. Agents communicate leading to increase of efficiencies of underachievers, and an efficiency of each agent can increase or decrease irrespectively of…
Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
The goal of the present study is to increase the intelligibility of macroeconomic phenomena triggered by governmental intervention in economy by means of fiscal policies. During cyclical movements, fiscal policy can play an important role…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
Economics has long been a science of static equilibria, in which time is a second-order rather than first-order concern. Without time, economic modelers may neglect or obscure the role of time-dependent phenomena, e.g. path-dependency, and…
One of the main tasks in the study of financial and economic processes is forecasting and analysis of the dynamics of these processes. Within this task lie important research questions including how to determine the qualitative properties…
Mathematical method based on a direct or indirect analysis of growth rates is described. It is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. Only…
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…