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Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity
Joint Authors
Siriwardena, Pathiranage Lochana
Hughes, Harry Randolph
Source
International Journal of Stochastic Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-02
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We consider stochastic differential equations with additive noise and conditions on the coefficients in those equations that allow a time singularity in the drift coefficient.
Given a maximum step size, h*, we specify variable (adaptive) step sizes relative to h* which decrease as the time node points approach the singularity.
We use an Euler-type numerical scheme to produce an approximate solution and estimate the error in the approximation.
When the solution is restricted to a fixed closed time interval excluding the singularity, we obtain a global pointwise error of order Oh*.
An order of error Oh*p for any p<1 is obtained when the approximation is run up to a time within h*q of the singularity for an appropriate choice of exponent q.
We apply this scheme to Brownian bridge, which is defined as the nonanticipating solution of a stochastic differential equation of the type under consideration.
In this special case, we show that the global pointwise error is of order Oh*, independent of how close to the singularity the approximation is considered.
American Psychological Association (APA)
Hughes, Harry Randolph& Siriwardena, Pathiranage Lochana. 2014. Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity. International Journal of Stochastic Analysis،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-503464
Modern Language Association (MLA)
Hughes, Harry Randolph& Siriwardena, Pathiranage Lochana. Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity. International Journal of Stochastic Analysis No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-503464
American Medical Association (AMA)
Hughes, Harry Randolph& Siriwardena, Pathiranage Lochana. Efficient Variable Step Size Approximations for Strong Solutions of Stochastic Differential Equations with Additive Noise and Time Singularity. International Journal of Stochastic Analysis. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-503464
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503464