Related papers: Change Point Testing for the Drift Parameters of a…
In this paper, we propose a drift-diffusion process on the probability simplex to study stochastic fluctuations in probability spaces. We construct a counting process for linear detailed balanced chemical reactions with finite species such…
We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under…
In this paper, a purely measurement-based method is proposed to estimate the dynamic system state matrix by applying the regression theorem of the multivariate Ornstein-Uhlenbeck process. The proposed method employs a recursive algorithm to…
We investigate the problem of estimating the drift parameter of a high-dimensional L\'evy-driven Ornstein--Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the minimax optimal rate of…
In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…
A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
Data drift is the change in model input data that is one of the key factors leading to machine learning models performance degradation over time. Monitoring drift helps detecting these issues and preventing their harmful consequences.…
This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…
High-dimensional time series are characterized by a large number of measurements and complex dependence, and often involve abrupt change points. We propose a new procedure to detect change points in the mean of high-dimensional time series…
This paper considers the problem of minimizing the time average of a stochastic process subject to time average constraints on other processes. A canonical example is minimizing average power in a data network subject to multi-user…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
An alpha-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter alpha>0 represents a mean reversion force to zero. We generalize the notion of alpha-Wiener bridges to continuous functions…
We consider a perturbation of a Hilbert space-valued Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
This paper introduces the generalized Hausman test as a novel method for detecting non-normality of the latent variable distribution of unidimensional Item Response Theory (IRT) models for binary data. The test utilizes the pairwise maximum…
In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter…
Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also…
We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.
Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully…