Related papers: Economic Growth Model with Constant Pace and Dynam…
How to compute (super) hedging costs in rather general fi- nancial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
The Continuous Opinions and Discrete Actions (CODA) model has been widely used to study the emergence of extremism in social networks. However, this standard model has been shown to generate unrealistic extreme opinions due to the…
In this paper, we revisit the question of how the dynamic optimality of search trees should be defined in external memory. A defining characteristic of external-memory data structures is that there is a stark asymmetry between queries and…
We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any…
A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the…
Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at…
This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…
We analyze export data aggregated at world global level of 219 classes of products over a period of 39 years. Our main goal is to set up a dynamical model to identify and quantify plausible mechanisms by which the evolutions of the various…
Modern deep-learning training is not memoryless. Updates depend on optimizer moments and averaging, data-order policies (random reshuffling vs with-replacement, staged augmentations and replay), the nonconvex path, and auxiliary state…
Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building…
We study the emergence of correlations between $N$ components of the position of a diffusive walker in $N$ dimensions that starts at the origin and resets to previously visited sites with certain probabilities. This is equivalent to $N$…
The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the…
This paper extends Xing's (2023abcd) optimal growth models of catching-up economies from the case of production function switching to that of economic structure switching and argues how a country develops its economy by endogenous…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
Economic growth depends on capital investments and on investments in education and innovation. The model introduced here will specifiy aggregate output as determined by aggregate supply of capital and education investment. After formulating…
Recent model-free reinforcement learning algorithms have proposed incorporating learned dynamics models as a source of additional data with the intention of reducing sample complexity. Such methods hold the promise of incorporating imagined…
Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were…
This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these…