scholarly journals Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay Under Local Lipschitz Condition

2014 ◽  
Vol 32 (2) ◽  
pp. 207-228 ◽  
Author(s):  
Chaman Kumar ◽  
Sotirios Sabanis
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Lipschitz Condition ◽  
Local Lipschitz Condition ◽  
Equations With Delay

Numerical Method of Hybrid Stochastic Functional Differential Equations with the Local Lipschitz Coefficients

2011 ◽  
Vol 267 ◽  
pp. 422-426
Author(s):  
Hua Yang ◽  
Feng Jiang ◽  
Jun Hao Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Lipschitz Condition ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Stochastic Functional

Recently, hybrid stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical schemes established for the hybrid stochastic functional differential equations. In this paper, the Euler—Maruyama method is developed, and the main aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition. The result obtained generalizes the earlier results.

scholarly journals Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Lipschitz Condition ◽  
New Type ◽  
And Diffusion

We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.

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