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Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients

100%
Semrau A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2007
|
tom 55
|
nr 2
171-182
EN
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
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Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients

100%
Semrau A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 2
169-180
EN
We study $L^p$ convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ ℝ^d. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D=[0,∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.
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