Related papers: Generator Identification for Linear SDEs with Addi…

This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…

The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a…

The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large…

Learning predictors that do not rely on spurious correlations involves building causal representations. However, learning such a representation is very challenging. We, therefore, formulate the problem of learning a causal representation…

Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…

Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…

Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…

In this paper we establish a substitution formula for stochastic differential equation driven by generalized grey noise. We then apply this formula to investigate the absolute continuity of the solution with respect to the Lebesgue measure…

We consider the problem of causal discovery (a.k.a., causal structure learning) in a multi-domain setting. We assume that the causal functions are invariant across the domains, while the distribution of the exogenous noise may vary. Under…

This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the…

We present a general method to construct couplings of stochastic differential equations driven by L\'{e}vy noise in terms of coupling operators. This approach covers both coupling by reflection and refined basic coupling which are often…

We consider a non-linear parabolic partial differential equation (PDE) on $\mathbb R^d$ with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity…

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of…

In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise is analyzed.

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…

Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…

We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these…

In this work, by using Levi's parametrix method we first construct the fundamental solution of the critical non-local operator perturbed by gradient. Then, we use the obtained estimates to prove the existence and uniqueness of strong…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito stochastic…