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Your search keyword '"Liu, Jicheng"' showing total 3 results
Start Over Author "Liu, Jicheng" Topic stochastic differential equations Publisher elsevier b.v.
3 results on '"Liu, Jicheng"'

1. Carathéodory approximations and stability of solutions to non-Lipschitz stochastic fractional differential equations of Itô-Doob type.

Author

Abouagwa, Mahmoud, Liu, Jicheng, and Li, Ji

Subjects
*CARATHEODORY measure, *LIPSCHITZ spaces, *FRACTIONAL differential equations, *STOCHASTIC analysis, *MEAN square algorithms
Abstract

The existence and uniqueness theorem of solutions provides an effective tool for the model validation of both deterministic and stochastic equations. The objective of this paper is to establish the existence and uniqueness of solutions for a class of Itô-Doob stochastic fractional differential equations under non-Lipschitz condition which is weaker than Lipschitz one and contains it as a special case. The solution is constructed with the aid of Carathéodory approximation. Moreover, the continuous dependence of solutions on the initial value is investigated in view of the stability of solutions in the sense of mean square. Finally, an example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]

Published
2018
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2. [formula omitted]-convergence of Picard’s successive approximations to solutions of stochastic differential equations.

Author

Li, Zhen and Liu, Jicheng

Subjects
*STOCHASTIC differential equations, *STOCHASTIC convergence, *PICARD number, *APPROXIMATION theory, *COEFFICIENTS (Statistics)
Abstract

In this paper, we prove that for a stochastic differential equation with the coefficients of class C ∞ , the successive approximations of Picard converge in the C ∞ -sense, which implies that the solution to stochastic differential equation is of class C ∞ in the initial value x almost surely. [ABSTRACT FROM AUTHOR]

Published
2017
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3. Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient

Author

Liu, Jicheng and Ren, Jiagang

Subjects
*STOCHASTIC differential equations, *MATHEMATICAL statistics
Abstract

Comparison theorems for solutions of one-dimensional backward stochastic differential equations were established by Peng and Cao-Yan, where the coefficients were, respectively, required to be Lipschitz and Dini continuous. In this work, we generalize the comparison theorem to the case where the coefficient is only continuous. [Copyright &y& Elsevier]

Published
2002
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