Strong uniform Wong–Zakai approximations of Lévy-driven Marcus SDEs
Abstract
For the solution X of a Lévy-driven d-dimensional Marcus (canonical) stochastic differential equation, we prove that the Wong–Zakai approximation scheme Xh converges strongly with order 12. More precisely, for any T∈[0,∞) there exists a constant CT∈(0,∞) such that Esupkh∈[0,T]|Xkh(x)−Xkhh(x)|≤CTh12(1+|x|),h→0, for all x∈Rd. We also establish the rate of locally uniform strong convergence: for every T∈[0,∞) and any N∈(0,∞) there exists a constant CT,N∈(0,∞) such that Esup|x|≤Nsupkh∈[0,T]|Xkh(x)−Xkhh(x)|≤CT,Nh1−ε4d,h→0.
Fields of Study & Subjects
Stochastic processes and financial applications
Economic theories and models
Publication details
- Journal / source
- Stochastic Analysis and Applications
- Publisher
- Informa UK Limited
- Volume
- 44
- Issue
- 4
- Pages
- 476–498
- Publication date
- 25 May 2026
- Language
- EN