STOCHASTIC DIFFERENTIAL EQUATIONS WITH CONSTRAINTS
DRIVEN BY PROCESSES WITH BOUNDED -VARIATION
Adrian Falkowski
Leszek Słomiński
Abstract: We study the existence, uniqueness and approximation of solutions of stochastic
differential equations with constraints driven by processes with bounded -variation. Our
main tool are new estimates showing Lipschitz continuity of the deterministic Skorokhod
problem in -variation norm. Applications to fractional SDEs with constraints are given.
2000 AMS Mathematics Subject Classification: Primary: 60H20; Secondary:
60G22.
Keywords and phrases: Skorokhod problem, -variation, integral equations, stochastic
differential equations with constraints, reflecting boundary condition.