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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 Vol. 55, no 2

171-182

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.

Discrete approximations of strong solutions of reflecting SDEs with discontinuous coefficients

100%

Semrau A.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

tom Vol. 57, no 2

169-180

We study Lp convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ Rd. 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.

Stochastic differential equations with constraints driven by processes with bounded p-variation

88%

Falkowski A. , Słomiński L.

Probability and Mathematical Statistics

2015

tom Vol. 35, Fasc. 2

343--365

We study the existence, uniqueness and approximation of solutions of stochastic differential equations with constraints driven by processes with bounded p-variation. Our main tool are new estimates showing Lipschitz continuity of the deterministic Skorokhod problem in p-variation norm. Applications to fractional SDEs with constraints are given.