Donsker theorems for diffusions: Necessary and sufficient conditions
نویسندگان
چکیده
منابع مشابه
Donsker Theorems for Diffusions: Necessary and Sufficient Conditions
We consider the empirical process Gt of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F . By the central limit theorem for diffusions, the finite-dimensional distributions of Gt converge weakly to those of a zero-mean Gaussian random process G. We prove that the weak convergence Gt ⇒ G takes place in l(F) if and only if the limit G exists as a tight...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2005
ISSN: 0091-1798
DOI: 10.1214/009117905000000152