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Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions. (English) Zbl 1121.65011
The authors consider the stochastic differential equation with Markovian switching \[ dy(t)=f(y(t),r(t))dt+g(y(t),r(t))dw(t) \] where \(w(t)\) is a \(d\)-dimensional Brownian motion, \(r(t)\) is a right-continuous Markov chain, and \(w\) and \(r\) are independent. It is proved that the approximate solutions generated by the Euler-Maruyama numerical method converge in the \(L^1\) sense and the \(L^2\) sense under hypotheses sufficiently less restrictive to include some important equations arising in finance and engineering.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
60J65 Brownian motion
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