Convergence of numerical solutions to stochastic pantograph equations with Markovian switching (Q732504)
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scientific article; zbMATH DE number 5612913
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of numerical solutions to stochastic pantograph equations with Markovian switching |
scientific article; zbMATH DE number 5612913 |
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Convergence of numerical solutions to stochastic pantograph equations with Markovian switching (English)
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9 October 2009
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The authors investigate the convergence of the Euler method for \(n\)-dimensional stochastic pantograph equations with Markovian switching of the form \[ dx(t)=\mu(x(t),x(qt),r(t))dt+\sigma(x(t),x(qt),r(t))dB_{t}, \] where \(0<q<1,\;r(t)\) is a right-continuous Markov chain taking values in a finite set, \(B_{t}\) is a standard \(m\)-dimensional Brownian motion.
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stochastic pantograph equation
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Markovian switching
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Euler approximation
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convergence
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Markov chain
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Brownian motion
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