期刊文献+
共找到6篇文章
< 1 >
每页显示 20 50 100
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS 被引量:31
1
作者 PENG Shige 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第2期159-184,共26页
This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectatio... This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures. 展开更多
关键词 Backward stochastic differential equations nonlinear expectation Non-linear expected utilities Measure of risk G-expectation nonlinear Mar-kov chain g-martingale nonlinear martingale nonlinear Kolmogorov’s consistent theorem Doob-Meyer decomposition
原文传递
Law of large numbers and central limit theorem under nonlinear expectations 被引量:7
2
作者 Shige Peng 《Probability, Uncertainty and Quantitative Risk》 2019年第1期72-79,共8页
The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequenc... The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequence{1/√n(X1+···+Xn)}i∞=1 converges in law to a nonlinear normal distribution,called G-normal distribution,where{Xi}i∞=1 is an i.i.d.sequence under the sublinear expectation.It’s known that the framework of sublinear expectation provides a important role in situations that the probability measure itself has non-negligible uncertainties.Under such situation,this new CLT plays a similar role as the one of classical CLT.The classical CLT can be also directly obtained from this new CLT,since a linear expectation is a special case of sublinear expectations.A deep regularity estimate of 2nd order fully nonlinear parabolic PDE is applied to the proof of the CLT.This paper is originally exhibited in arXiv.(math.PR/0702358v1). 展开更多
关键词 Central limit theorem nonlinear expectation Probability measure uncertainty
原文传递
A Law of Large Numbers Under the Nonlinear Expectation 被引量:1
3
作者 Miao ZHANG Zeng-jing CHEN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第4期953-962,共10页
In this paper, we derive a law of large numbers under the nonlinear expectation generated by backward stochastic differential equations driven by G-Brownian motion.
关键词 law of large numbers nonlinear expectation backward stochastic differential equation
原文传递
Strong laws of large numbers for sub-linear expectations 被引量:26
4
作者 CHEN ZengJing 《Science China Mathematics》 SCIE CSCD 2016年第5期945-954,共10页
We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out... We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities. 展开更多
关键词 capacity strong law of large numbers independently and identically distributed nonlinear expectation
原文传递
Numerical simulations for G-Brownian motion 被引量:4
5
作者 Jie YANG Weidong ZHA0 《Frontiers of Mathematics in China》 SCIE CSCD 2016年第6期1625-1643,共19页
This paper is concerned with numerical simulations for the G- Brownian motion (defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567). By the definition of the G-normal distribution, we first sho... This paper is concerned with numerical simulations for the G- Brownian motion (defined by S. Peng in Stochastic Analysis and Applications, 2007, 541-567). By the definition of the G-normal distribution, we first show that the G-Brownian motions can be simulated by solving a certain kind of Hamilton-Jacobi-Bellman (HJB) equations. Then, some finite difference methods are designed for the corresponding HJB equations. Numerical simulation results of the G-normal distribution, the G-Brownian motion, and the corresponding quadratic variation process are provided, which characterize basic properties of the G-Brownian motion. We believe that the algorithms in this work serve as a fundamental tool for future studies, e.g., for solving stochastic differential equations (SDEs)/stochastic partial differential equations (SPDEs) driven by the G-Brownian motions. 展开更多
关键词 nonlinear expectation G-Brownian motion G-normal distribu- tion Hamilton-Jacobi-Bellman (HJB) equation
原文传递
Uncertainty and filtering of hidden Markov models in discrete time
6
作者 Samuel N.Cohen 《Probability, Uncertainty and Quantitative Risk》 2020年第1期68-101,共34页
We consider the problem of filtering an unseen Markov chain from noisy observations,in the presence of uncertainty regarding the parameters of the processes involved.Using the theory of nonlinear expectations,we descr... We consider the problem of filtering an unseen Markov chain from noisy observations,in the presence of uncertainty regarding the parameters of the processes involved.Using the theory of nonlinear expectations,we describe the uncertainty in terms of a penalty function,which can be propagated forward in time in the place of the filter.We also investigate a simple control problem in this context. 展开更多
关键词 FILTERING Optimal control ROBUSTNESS nonlinear expectation
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部