In 2007, Peng introduced Ito integral with respect to G-Brownian motion and the related Ito＇s formula in G-expectation space. Motivated by the properties of multiple Wiener integral obtained by Ito in 1951, we introd...In 2007, Peng introduced Ito integral with respect to G-Brownian motion and the related Ito＇s formula in G-expectation space. Motivated by the properties of multiple Wiener integral obtained by Ito in 1951, we introduce multiple G-Ito integral in G-expectation space, and investigate how to calculate it. Furthermore, We establish a relationship between Hermite polynomials and multiple G-Ito integrals.展开更多
The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equ...The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equation. Another type of stochastic integral equation which has been of considerable importance to applied mathematicians and engineers is that involving the It? or It?-Doob form of stochastic integrals.展开更多
Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random...Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.展开更多
The main aim of this paper is to present and emphasize the contribution of stochastic numerical methods as must tools for the modern econometric modelisation. Indeed, the stochastic numerical methods play an important...The main aim of this paper is to present and emphasize the contribution of stochastic numerical methods as must tools for the modern econometric modelisation. Indeed, the stochastic numerical methods play an important role in mathematical modelling and the econometric analysis because they model uncertainties that govern the real-world data. However these powerful tools are not well-known and understood by many economists and financial econometricians.展开更多
In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equat...In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.展开更多
文摘In 2007, Peng introduced Ito integral with respect to G-Brownian motion and the related Ito＇s formula in G-expectation space. Motivated by the properties of multiple Wiener integral obtained by Ito in 1951, we introduce multiple G-Ito integral in G-expectation space, and investigate how to calculate it. Furthermore, We establish a relationship between Hermite polynomials and multiple G-Ito integrals.
文摘The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equation. Another type of stochastic integral equation which has been of considerable importance to applied mathematicians and engineers is that involving the It? or It?-Doob form of stochastic integrals.
基金Project supported by the National Natural Science Foundation of China(Grant No.61273015)
文摘Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.
文摘The main aim of this paper is to present and emphasize the contribution of stochastic numerical methods as must tools for the modern econometric modelisation. Indeed, the stochastic numerical methods play an important role in mathematical modelling and the econometric analysis because they model uncertainties that govern the real-world data. However these powerful tools are not well-known and understood by many economists and financial econometricians.
文摘In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.
