Related papers: Measure-valued affine and polynomial diffusions
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
As deep generative models proliferate across the AI landscape, industrial practitioners still face critical yet unanswered questions about which deep generative models best suit complex manufacturing design tasks. This work addresses this…
In this paper, we derive a representation for the value process associated to the solutions of FBSDEs in a jump-diffusion setting under multiple probability measures. Motivated by concrete financial problems, the latter representations are…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Continuing the ideas from our previous paper, we construct Parseval frames of weighted exponential functions for self-affine measures.
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
Diffusion-based methods represented as stochastic differential equations on a continuous-time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…
Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…
The theory of affine processes on the space of positive semidefinite d x d matrices has been established in a joint work with Cuchiero, Filipovi\'c and Teichmann (2011). We confirm the conjecture stated therein that in dimension d greater…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily…