Related papers: Anomalous Fluctuations in Autoregressive Models wi…
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…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spike-train itself can be…
The generalized Langevin equation (GLE) is a universal model for particle velocity in a viscoelastic medium. In this paper, we consider the GLE family with fractional memory kernels. We show that, in the critical regime where the memory…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with…
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…
Understanding characteristics of temporal correlations in time series is crucial for developing accurate models in natural and social sciences. The burst-tree decomposition method was recently introduced to reveal higher-order temporal…
In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…
We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…
Autoregressive neural network models have been used successfully for sequence generation, feature extraction, and hypothesis scoring. This paper presents yet another use for these models: allocating more computation to more difficult…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
The idea of using metaplastic synapses to incorporate the separate storage of long- and short-term memories via an array of hidden states was put forward in the cascade model of Fusi et al. In this paper, we devise and investigate two…
A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits anomalous…
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a $\beta$-power time change in the classical Fr\'echet extremal process, for $\beta$ in a subinterval of…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…