Related papers: From the Stochastic Embedding Sufficiency Theorem …

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a…

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of…

In this article, we address the absorption properties of a class of stochastic differ- ential equations around singular points where both the drift and diffusion functions vanish. According to the H\"older coefficient alpha of the diffusion…

We give a summary of the status of current research in stochastic semiclassical gravity and suggest directions for further investigations. This theory generalizes the semiclassical Einstein equation to an Einstein-Langevin equation with a…

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence…

We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…

Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

A Response Function Theory and Scattering Theory applicable to the study of physical properties of systems driven arbitrarily away from equilibrium, specialized for dealing with ultrafast processes and in conditions of space resolution…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the…

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…

Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

We present a complete framework of stochastic thermodynamics for a single-mode linear optical cavity driven on resonance. We first show that the steady-state intra-cavity field follows the equilibrium Boltzmann distribution. The effective…