• Corpus ID: 15546914

A New Central Limit Theorem under Sublinear Expectations

@article{Peng2008ANC,
  title={A New Central Limit Theorem under Sublinear Expectations},
  author={Shige Peng},
  journal={arXiv: Probability},
  year={2008}
}
  • S. Peng
  • Published 18 March 2008
  • Mathematics
  • arXiv: Probability
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty. 

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References

SHOWING 1-10 OF 25 REFERENCES

Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation. Many results can

G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

We introduce a new notion of G-normal distributions. This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) through the

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent

G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type

We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution.

A strong law of large numbers for capacities

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the

A THEORETICAL FRAMEWORK FOR THE PRICING OF CONTINGENT CLAIMS IN THE PRESENCE OF MODEL UNCERTAINTY

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a

User’s guide to viscosity solutions of second order partial differential equations

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence

Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims

We will study the following problem. Let Xt, t ∈ [0, T], be an Rd–valued process defined on a time interval t ∈ [0, T]. Let Y be a random value depending on the trajectory of X. Assume that, at each