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

Falkowski A., Słomiński L.

Probability and Mathematical Statistics

2015

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.

Approximation of solutions of SDE's with oblique reflection on an orthant

Czarkowski K., Słomiński L.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 1

29--49

We consider the discrete penalization scheme, the projection and the Euler-Peano scheme for SDE’s driven by general semimartingale on an orthant with oblique reflection. We prove that these schemes converge in probability to the solution of the SDE in various topologies provided that the oblique reflection satisfies theassumption introduced by Harrison and Reiman. In the case where the driving semimartingale is an Itô process, the rate of Lp-convergence is discussed in detail.