Stochastic differential delay equations with jumps, under nonlinear growth condition

DOI10.1080/17442500903251832zbMath1191.60081OpenAlexW2007452825MaRDI QIDQ5190573

Yongtian Wang, Chenggui Yuan, Niels Jacob

Publication date: 18 March 2010

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442500903251832

zbMATH Keywords

Lipschitz conditionItô's formulastochastic theta methodEuler-Maruyama method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability theory of functional-differential equations (34K20) Stochastic functional-differential equations (34K50) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

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Cites Work

• Unnamed Item
• Applied stochastic control of jump diffusions.
• Pricing contingent claims on stocks driven by Lévy processes
• A note on the LaSalle-type theorems for stochastic differential delay equations
• Numerical solutions of stochastic differential delay equations under local Lipschitz condition
• Approximate solutions of stochastic differential delay equations with Markovian switching
• Numerical Solutions of Stochastic Differential Delay Equations with Jumps
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Khasminskii-Type Theorems for Stochastic Differential Delay Equations

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