Related papers: Large deviations of the stochastic area for linear…
In this paper, we are interested in the propagation of convexity by the strong solution to a one-dimensional Brownian stochastic differential equation with coefficients Lipschitz in the spatial variable uniformly in the time variable and in…
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $\epsilon$ and $\delta$: the evolution equation contains singular terms with respect to $\epsilon$, and is driven by a fast ergodic…
Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
It is well understood that, when numerically simulating SDEs with general noise, achieving a strong convergence rate better than $O(\sqrt{h})$ (where h is the step size) requires the use of certain iterated integrals of Brownian motion,…
This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
In this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To…
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by…
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…
Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…