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We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state.…
This paper studies the zero-noise limit of high-dimensional small-noise diffusion processes governed by the stochastic differential equation (SDE): \[ dX_{t}^{\varepsilon }=b(X_{t}^{\varepsilon })\,dt+\varepsilon \,dW_{t}, \quad…
In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an…
Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…
While many real-world data streams imply that they change frequently in a nonstationary way, most of deep learning methods optimize neural networks on training data, and this leads to severe performance degradation when dataset shift…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
Out-of-Distribution (OoD) detection aims to justify whether a given sample is from the training distribution of the classifier-under-protection, i.e., In-Distribution (InD), or from OoD. Diffusion Models (DMs) are recently utilized in OoD…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
Out-of-distribution (OOD) detection is a crucial task for ensuring the reliability and safety of deep learning. Currently, discriminator models outperform other methods in this regard. However, the feature extraction process used by…
In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are…
We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…