A Note on Euler Approximations for Stochastic Differential Equations with Delay

Istvan Gyongy; Sotirios Sabanis

doi:10.1007/s00245-013-9211-7

A Note on Euler Approximations for Stochastic Differential Equations with Delay

Istvan Gyongy, Sotirios Sabanis

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.

Original language	English
Pages (from-to)	391-412
Journal	Applied Mathematics and Optimization
Volume	68
Issue number	3
Early online date	24 Aug 2013
DOIs	https://doi.org/10.1007/s00245-013-9211-7
Publication status	Published - Dec 2013

Keywords / Materials (for Non-textual outputs)

Stochastic delay differential equations
Euler approximations
Rate of convergence
Local Lipschitz condition
Monotonicity condition

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10.1007/s00245-013-9211-7

A Note on Euler Approximations for Stochastic Differential Equations with Delay
The final publication is available at Springer via http://dx.doi.org/10.1007/s00245-013-9211-7
Accepted author manuscript, 288 KB

http://link.springer.com/article/10.1007%2Fs00245-013-9211-7

Cite this

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title = "A Note on Euler Approximations for Stochastic Differential Equations with Delay",

abstract = "An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.",

keywords = "Stochastic delay differential equations , Euler approximations, Rate of convergence, Local Lipschitz condition, Monotonicity condition",

author = "Istvan Gyongy and Sotirios Sabanis",

year = "2013",

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T1 - A Note on Euler Approximations for Stochastic Differential Equations with Delay

AU - Gyongy, Istvan

AU - Sabanis, Sotirios

PY - 2013/12

Y1 - 2013/12

N2 - An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.

AB - An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.

KW - Stochastic delay differential equations

KW - Euler approximations

KW - Rate of convergence

KW - Local Lipschitz condition

KW - Monotonicity condition

U2 - 10.1007/s00245-013-9211-7

DO - 10.1007/s00245-013-9211-7

M3 - Article

SN - 0095-4616

VL - 68

SP - 391

EP - 412

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 3

ER -

A Note on Euler Approximations for Stochastic Differential Equations with Delay

Abstract

Keywords / Materials (for Non-textual outputs)

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