相关论文: Local Strict Comparison Theorem and Converse Compa…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the…
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…
This work deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression-later approach and the least squares Monte Carlo method. We give some…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
The paper deals with the existence and uniqueness of the solution of the backward stochastic variational inequality: \begin{equation} \left\{\begin{array} {l}-dY_{t}+\partial \varphi(Y_{t})dt \ni F(t,Y_{t},Z_{t})dt-Z_{t}dB_{t},\;0\leq t<T…
We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…
In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes…
Contrastive learning is an approach to representation learning that utilizes naturally occurring similar and dissimilar pairs of data points to find useful embeddings of data. In the context of document classification under topic modeling…
Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, {\phi} : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that…
Following the work of Jean-Loup Waldspurger, we prove the epsilon dichotomy part of the local Gross-Prasad conjecture over $\mathbb{R}$ for tempered local $L$-parameters.
The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a…
Bounds on Bayesian posterior convergence rates, assuming the prior satisfies both local and global support conditions, are now readily available. In this paper we explore, in the context of density estimation, Bayesian convergence rates…
This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…
We give a proof of the Howe duality conjecture in local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic.
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…