相关论文: Wavelet entropy of stochastic processes

This PhD thesis deals with the Markov picture of developed turbulence from the theoretical point of view. The thesis consists of two parts. The first part introduces stochastic thermodynamics, the second part aims at transferring the…

Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…

We propose a transfer principle to study the adapted 2-Wasserstein distance between stochastic processes. First, we obtain an explicit formula for the distance between real-valued mean-square continuous Gaussian processes by introducing the…

When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic…

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…

Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational…

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

Nucleation, the birth of a stable cluster from disorder, is inherently stochastic. Yet up to date, there are no quantitative studies on NaCl nucleation that accounts for its stochastic nature. Here, we report the first stochastic treatment…

Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise…

Following [1], the aim of this paper is to analyze the relative weighted entropy involving the central moments weight functions. We compare the standard relative entropy with the weighted case in two particular forms of Gaussian…

Based on the wavelet-defined multiscale random noise proposed in [Doklady Physics 2003, v.48, 478], a multiscale version of the stochastic quantization procedure is considered. A new type of the commutation relations emerging from the…

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

Noise aids the encoding of continuous signals into pulse sequences by way of stochastic resonance and endows the encoding device with a preferred frequency. We study encoding by a threshold device based on the Ornstein-Uhlenbeck process,…

Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity…

The recent detection of nanohertz stochastic gravitational-wave backgrounds (SGWBs) by pulsar timing arrays (PTAs) promises unique insights into astrophysical and cosmological origins. However, traditional Markov Chain Monte Carlo (MCMC)…

In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend…