Numerical methods for backward stochastic differential equations: A survey

J Chessari, R Kawai, Y Shinozaki… - Probability Surveys, 2023 - projecteuclid.org
Abstract Backward Stochastic Differential Equations (BSDEs) have been widely employed in
various areas of social and natural sciences, such as the pricing and hedging of financial …

Score-based generative modeling through backward stochastic differential equations: Inversion and generation

Z Wang - arXiv preprint arXiv:2304.13224, 2023 - arxiv.org
The proposed BSDE-based diffusion model represents a novel approach to diffusion
modeling, which extends the application of stochastic differential equations (SDEs) in …

Dynamic Bayesian network modeling based on structure prediction for gene regulatory network

L Qu, Z Wang, C Li, S Guo, J Xin, Y Zhou… - IEEE Access, 2021 - ieeexplore.ieee.org
Gene regulatory network can intuitively reflect the interaction between genes, and an in-
depth study of these relationships plays a significant role in the treatment and prevention of …

[HTML][HTML] Density analysis of non-Markovian BSDEs and applications to biology and finance

T Mastrolia - Stochastic Processes and their Applications, 2018 - Elsevier
In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit
Malliavin differentiable solutions. We investigate the problem of existence of densities for the …

基因调控网络的父节点筛选贝叶斯建模方法.

曲璐渲, 郭上慧, 王之琼… - Journal of Northeastern …, 2020 - search.ebscohost.com
在构建基因调控网络的方法中ꎬ 贝叶斯网络模型可以直观地表达基因间的调控关系ꎬ
但在结构学习时的复杂度极高ꎬ 使得网络建模效率较低且规模有限. 因此ꎬ 本文提出一种基于父 …

Distributed local Bayesian network for gene regulatory network reconstruction

L Qu, Z Wang, Y Huo, Y Zhou, J Xin… - 2020 6th International …, 2020 - ieeexplore.ieee.org
Gene regulatory network provides an effective way to study functional genomes.
Reconstruction of gene regulatory network can better help us to reveal the regulatory …

Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression

R Chertovskih, E Shamarova - Potential Analysis, 2023 - Springer
We obtain upper and lower Gaussian-type bounds on the density of each component Y ti of
the solution Y t to a multidimensional non-Markovian backward SDE. Our approach is based …

[PDF][PDF] G-Framework in statistics

Y Sale - 2022 - epub.ub.uni-muenchen.de
In order to achieve reliable results via statistical methodology, one important goal is to
account for potential uncertainty. Shige Peng introduced an uncertainty counterpart of …

Sampling of Stochastic Differential Equations using the Karhunen-Lo\eve Expansion and Matrix Functions

A Koskela, SD Relton - arXiv preprint arXiv:2004.05687, 2020 - arxiv.org
We consider linearizations of stochastic differential equations with additive noise using the
Karhunen-Lo\eve expansion. We obtain our linearizations by truncating the expansion and …