Related papers: Propagation of Memory Parameter from Durations to …
Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also…
The fractional difference operator remains to be the most popular mechanism to generate long memory due to the existence of efficient algorithms for their simulation and forecasting. Nonetheless, there is no theoretical argument linking the…
Animals behave adaptively in the environment with multiply competing goals. Understanding of the mechanisms underlying such goal-directed behavior remains a challenge for neuroscience as well for adaptive system research. To address this…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To…
We propose a minimal yet intriguing model for a relationship between two individuals. The feeling of an individual is modeled by a complex variable and hence has two degrees of freedom. The effect of memory of other individual's behavior in…
We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set…
In this paper, a new approach to bivariate modeling of autoregressive conditional duration (ACD) models is proposed. Specifically, we consider the joint modeling of durations and the number of transactions made during the spell. The…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots…
We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as a simplified models…
The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory…
In order for large language models to achieve true conversational continuity and benefit from experiential learning, they need memory. While research has focused on the development of complex memory systems, it remains unclear which types…
We propose a dynamical approach to quantum memories using an oscillator-cavity model. This overcomes the known difficulties of achieving high quantum input-output fidelity with storage times long compared to the input signal duration. We…
We present an inequality that bounds the short-term memory capability of dynamical systems from below. It can be interpreted as an uncertainty relation between a measure of short-term memory and that of the size of state fluctuations…
We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…