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Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized rando...
In this paper we study the academician Peng Shige's papers of the nonlinear expectation since 2005. Under this foundation we interpret some theories and resolve several problems of the theory of G-exp...
Abstract: A classic theorem of T. Ando characterises operators that have numerical radius at most one as operators that admit a certain positive 2x2 operator matrix completion. In this paper we consid...
In this paper, motivated by mathematic finance we introduce the multiple G-Itˆo integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite...
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists su...
This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is stablished to provide pro...
Our purpose is to investigate properties for processes with stationary and independent increments under G-expectation. As applications,we prove the martingale characterization to G-Brownian motion and...
The purpose of this article is to study the mathematical expectation of probabilistic metric space and by using the method of mathematical expectation to study the fixed point theorem of Banach in the...
In this work, we present results of Almost Sure Convergence and in Quadratic Mean of the gradient stochastic process for the sequential estimation of a conditional expectation. This work is motived b...
We show that the expectation of a class of functions of the sum of weighted identically independent distributed positive random variables is Schur-concave with respect to the weights. Furthermore, we ...
Some inequalities for the expectation and variance of a random variable whose p.d.f. is n-time differentiable are given.

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