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We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
We explore unsupervised speech enhancement using diffusion models as expressive generative priors for clean speech. Existing approaches guide the reverse diffusion process using noisy speech through an approximate, noise-perturbed…
Foundation models, particularly Large Language Models (LLMs), have revolutionized text and video processing, yet time series data presents distinct challenges for such approaches due to domain-specific features such as missing values,…
The objective of this paper is to give conditions ensuring that the backward partial integro differential equation associated with a multidimensional jump-diffusion with a pure jump component has a unique classical solution; that is the…
Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
Diffusion models are the mainstream approach for time series generation tasks. However, existing diffusion models for time series generation require retraining the entire framework to introduce specific conditional guidance. There also…
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting random walks can be quite different however. The diffusion coefficient can be made responsible for the size of jumps or…
We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a…
Short-term precipitation forecasting remains challenging due to the difficulty in capturing long-term spatiotemporal dependencies. Current deep learning methods fall short in establishing effective dependencies between conditions and…
The classical reduced-form and filtration expansion framework in credit risk is extended to the case of multiple, non-ordered defaults, assuming that conditional densities of the default times exist. Intensities and pricing formulas are…
Standard models of asset price dynamics, such as geometric Brownian motion (see, for example, Osborne, 1959, Samuelson, 2016), do not formally incorporate investor inertia. This paper presents a two-stage framework for modelling this…
We investigate under which conditions a single simulation of joint default times at a final time horizon can be decomposed into a set of simulations of joint defaults on subsequent adjacent sub-periods leading to that final horizon. Besides…
We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs…
This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…
Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality…