Pathwise convergence rates for numerical solutions of Markovian switching stochastic differential equations

This work develops numerical approximation algorithms for solutions of stochastic differential equations with Markovian switching. The existing numerical algorithms all use a discrete-time Markov chain for the approximation of the continuous-time Markov chain. In contrast, we generate the continuous...

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Veröffentlicht in:Nonlinear analysis: real world applications Jg. 13; H. 3; S. 1170 - 1185
Hauptverfasser: Nguyen, Son Luu, Yin, G.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.06.2012
Schlagworte:
Approximation
Convergence
Differential equations
Markov chains
Mathematical analysis
Mathematical models
Numerical method
Pathwise weak approximation
Stochastic differential equation
Stochasticity
Strong invariance principle
Switching
Strong invariance principle
Pathwise weak approximation
Numerical method
Stochastic differential equation
ISSN:1468-1218, 1878-5719
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Zusammenfassung:This work develops numerical approximation algorithms for solutions of stochastic differential equations with Markovian switching. The existing numerical algorithms all use a discrete-time Markov chain for the approximation of the continuous-time Markov chain. In contrast, we generate the continuous-time Markov chain directly, and then use its skeleton process in the approximation algorithm. Focusing on weak approximation, we take a re-embedding approach, and define the approximation and the solution to the switching stochastic differential equation on the same space. In our approximation, we use a sequence of independent and identically distributed (i.i.d.) random variables in lieu of the common practice of using Brownian increments. By virtue of the strong invariance principle, we ascertain rates of convergence in the pathwise sense for the weak approximation scheme.
Bibliographie:ObjectType-Article-2
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2011.09.012