相关论文: Large deviation properties of the empirical measur…

In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events related to random perturbation of ODE…

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift…

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…

Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…

In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…

The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

We study in this paper the large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multi-classes. The empirical vector is composed of local empirical measures characterizing the…

This paper reinterprets Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. Through a one-dimensional irreversible diffusion process on a…

In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…

This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

We consider a reduced order model of an air-breathing hypersonic engine with a time-dependent stochastic inflow that may cause the failure of the engine. The probability of failure is analyzed by the Freidlin-Wentzell theory, the large…

To synthesize diffusion MR measurements from Monte-Carlo simulation using tissue models with sizes comparable to those of scan voxels. Larger regions enable restricting structures to be modeled in greater detail and improve accuracy and…

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity…

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…