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

DOI10.1080/07362994.2014.858552zbMath1291.60142arXiv1303.0017OpenAlexW2964200623MaRDI QIDQ5413859

Chaman Kumar, Sotirios Sabanis

Publication date: 2 May 2014

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0017

zbMATH Keywords

rate of convergencestrong convergencelocal Lipschitz conditionstochastic delay differential equationsEuler approximations

Mathematics Subject Classification ID

Stochastic functional-differential equations (34K50) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (6)

Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth ⋮ On the approximations of solutions to stochastic differential equations under polynomial condition ⋮ Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments ⋮ On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps ⋮ On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations ⋮ The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations

Cites Work

• Unnamed Item
• A stochastic control problem with delay arising in a pension fund model
• Optimal stopping of stochastic differential equations with delay driven by Lévy noise
• Convergence rate of numerical solutions to SFDEs with jumps
• A note on Euler's approximations
• Coherence of noisy oscillators with delayed feedback
• Weak discrete time approximation of stochastic differential equations with time delay
• Numerical solutions of stochastic differential delay equations under local Lipschitz condition
• Discrete-time approximations of stochastic delay equations: the Milstein scheme.
• A note on Euler approximations for stochastic differential equations with delay
• Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations
• Convergence rate of EM scheme for \normalfont𝑆𝐷𝐷𝐸𝑠
• Arithmetic Asian Options under Stochastic Delay Models
• Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations
• The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations
• Weak Convergence of the Euler Scheme for Stochastic Differential Delay Equations
• Existence and uniqueness of solutions of stochastic functional differential equations
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• A Delayed Black and Scholes Formula
• On stochastic equations with respect to semimartingales I.^†
• Weak approximation of stochastic differential delay equations
• A Simple Proof of the Existence of a Solution of Itô’s Equation with Monotone Coefficients
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Numerical Solutions of Stochastic Functional Differential Equations

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