Related papers: Fractional Bessel Process with Constant Drift: Spe…
Time-changed stochastic processes have attracted great attention and wide interests due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process,…
We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for…
We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficient,…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
We construct a random partition of the space-time plane $\mathbb{R}_+\times \mathbb{R}$ using two coupled stochastic squared Bessel flows, whose parameters differ by $\delta\in (0,2)$. We show that the cells of this partition correspond to…
In this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS) method with time varying parameters adapted from the distribution of the data. In this approach, we employ Non-Stationary Fuzzy Sets, in which perturbation functions are…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…