scholarly journals The improved split-step backward Euler method for stochastic differential delay equations

2011 ◽  
Vol 88 (11) ◽  
pp. 2359-2378 ◽  
Author(s):  
Xiaojie Wang ◽  
Siqing Gan
Keyword(s):  
Euler Method ◽  
Delay Equations ◽  
Backward Euler Method ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Backward Euler

scholarly journals Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Minghui Song ◽  
Hui Yu
Keyword(s):  
Numerical Solutions ◽  
Random Measure ◽  
Global Solutions ◽  
Euler Method ◽  
Delay Equations ◽  
Poisson Random Measure ◽  
Differential Delay ◽  
Numerical Example ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results.

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