Related papers: Change point inference in ergodic diffusion proces…
A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution $f_{\theta}$ and tries to minimize the detection delay for every possible post-change…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
It is argued that a diffusion may be ergodic even though the drift field has unbounded outward-directed parts. The discussion employs stochastic and numerical methods.
We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…
We consider two problems of constructing of goodness of fit tests for ergodic diffusion processes. The first one is concerned with a composite basic hypothesis for a parametric class of diffusion processes, which includes the…
Existing monitoring tools for multivariate data are often asymptotically distribution-free, computationally intensive, or require a large stretch of stable data. Many of these methods are not applicable to 'high dimension, low sample size'…
In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…
We consider the goodness of fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We…
We study a statistical procedure based on higher criticism (HC) to address the sparse multi-stream quickest change-point detection problem. Namely, we aim to detect a potential change in the distribution of multiple data streams at some…
Data distributions in streaming environments are usually not stationary. In order to maintain a high predictive quality at all times, online learning models need to adapt to distributional changes, which are known as concept drift. The…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…
A change points detection aims to catch an abrupt disorder in data distribution. Common approaches assume that there are only two fixed distributions for data: one before and another after a change point. Real-world data are richer than…
We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change…
This paper considers the detection of change points in parallel data streams, a problem widely encountered when analyzing large-scale real-time streaming data. Each stream may have its own change point, at which its data has a…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…