Zobrazeno 1 - 10
of 283
pro vyhledávání: '"Peng, Shige"'
We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear expectation sy
Externí odkaz:
http://arxiv.org/abs/2411.03512
Autor:
Ji, Xiaojun, Peng, Shige
In this paper, we study the stochastic heat equation driven by a multiplicative space-time $G$-white noise within the framework of sublinear expectations. The existence and uniqueness of the mild solution are proved. By generalizing the stochastic Fu
Externí odkaz:
http://arxiv.org/abs/2407.17806
The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators revealed that mo
Externí odkaz:
http://arxiv.org/abs/2403.12647
This article establishes a universal robust limit theorem under a sublinear expectation framework. Under moment and consistency conditions, we show that, for $\alpha \in(1,2)$, the i.i.d. sequence \[ \left \{ \left( \frac{1}{\sqrt{n}}\sum_{i=1}^{n}X_
Externí odkaz:
http://arxiv.org/abs/2205.00203
In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first transform the
Externí odkaz:
http://arxiv.org/abs/2204.05796
Autor:
Li, Xinpeng, Peng, Shige
This paper focuses on the maximal distribution on sublinear expectation space and introduces a new type of random fields with the maximally distributed finite-dimensional distribution. The corresponding spatial maximally distributed white noise is co
Externí odkaz:
http://arxiv.org/abs/2202.10699
A novel control method for solving high-dimensional Hamiltonian systems through deep neural networks
In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from the view of
Externí odkaz:
http://arxiv.org/abs/2111.02636
Autor:
Peng, Shige, Yang, Shuzhen
Based on law of large numbers and central limit theorem under nonlinear expectation, we introduce a new method of using G-normal distribution to measure financial risks. Applying max-mean estimators and small windows method, we establish autoregressi
Externí odkaz:
http://arxiv.org/abs/2011.09226
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum co
Externí odkaz:
http://arxiv.org/abs/2007.02227