Crossings and occupation measures for a class of semimartingales

• 成果类型: Article
• 署名作者: Perera, G; Wschebor, M
• 署名单位: Universite Paris Saclay; Universidad de la Republica, Uruguay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 253-266
• 关键词: local time; wiener

摘要

We show that 1/root epsilon {integral(-infinity)(infinity) f(u)k(epsilon)N(tau)(X epsilon)(u) du - integral(0)(tau) f(X-t)a(t)dt} converges in law (as a continuous process) to c(psi) f(0)(tau) f(X-t)a(t) dB(t), where X-t = integral(0)(t) a(s) dW(s) + integral(0)(t) b(s) ds, with W a standard Brownian motion, a. and b regular and adapted processes, X-epsilon(t) = integral(-infinity)(infinity)(1/epsilon)psi((t - u)/epsilon)X-u du, psi a smooth kernel, N-t(g)(u) the number of roots of the equation g(s) = u, s is an element of (0, t], k(epsilon) = root pi epsilon\2\parallel to(2), f a smooth function, B a standard Brownian motion independent of W and c(psi) a constant depending only on psi.