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Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation.…
We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…
Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad…
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator $g$ satisfies a weak…
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The…
We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors, which follow a linear structural causal model. Recent work has shown that it is possible to recover the latent…
Diffusion models have proven effective for various applications such as images, audio and graph generation. Other important applications are image super-resolution and the solution of inverse problems. More recently, some works have used…
Guided image synthesis enables everyday users to create and edit photo-realistic images with minimum effort. The key challenge is balancing faithfulness to the user input (e.g., hand-drawn colored strokes) and realism of the synthesized…
Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the…
We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators singular in $ y $. First, we establish the existence of solutions and a comparison theorem, thereby extending results in the literature.…
This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator $g$ has a quadratic growth in the unknown variable $z$ and…
In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear…
This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate…
Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…
Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear…
This paper aims to address the challenge of data generation beyond the training data and proposes a framework for Structural Extrapolated Data GEneration (SEDGE) based on suitable assumptions on the underlying data-generating process. We…
Generative models have attracted considerable attention for speech separation tasks, and among these, diffusion-based methods are being explored. Despite the notable success of diffusion techniques in generation tasks, their adaptation to…