Related papers: Aggregation of autoregressive processes and long m…
Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and…
In this thesis, we analyse the generalisations of the Ornstein-Uhlenbeck (OU) semigroup and study them in both quantum and classical setups. In the first three chapters, we analyse the dissipative dynamics on noncommutative/quantum spaces,…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
Autoregressive video diffusion models enable streaming generation, opening the door to long-form synthesis, video world models, and interactive neural game engines. However, their core attention layers become a major bottleneck at inference…
We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent `seed' processes on shrinking intervals (`trawl heights'). Related trawl processes in…
Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, associative memories for sparse patterns, such…
Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…
A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is…
Recent work by Marino et al. (2020) showed improved performance in sequential density estimation by combining masked autoregressive flows with hierarchical latent variable models. We draw a connection between such autoregressive generative…
We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network…
A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…
We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that…
We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of…
We study the long time behavior of an advection-diffusion equation with a random shear flow which depends on a stationary Ornstein-Uhlenbeck (OU) process in parallel-plate channels enforcing the no-flux boundary conditions. We derive a…
An autoregressive model with a power-law type memory kernel is studied as a stochastic process that exhibits a self-affine-fractal-like behavior for a small time scale. We find numerically that the root-mean-square displacement for the time…
In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the…
We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin…
We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required…
Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…
Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…