Small time Edgeworth-type expansions for weakly convergent nonhomogeneous Markov chains

• 成果类型: Article
• 署名作者: Konakov, Valentin; Mammen, Enno
• 署名单位: University of Mannheim; Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0123-9
• 发表日期: 2009
• 页码: 137-176
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; berry-esseen theorem; LIMIT-THEOREMS; euler scheme; asymptotic expansions; transition densities; distributions; functionals; DIFFUSIONS

摘要

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are motivated by statistical applications and by resulting approximations for the joint density of diffusion values at an increasing grid of points.