Related papers: Discrete-Time Statistical Inference for Multiscale…

The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation…

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…

We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i)…

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to…

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…

Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

The increasing complexity of distribution network calls for advancement in distribution system state estimation (DSSE) to monitor the operating conditions more accurately. Sufficient number of measurements is imperative for a reliable and…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…

Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…