On the number of crossings of some levels by a sequence of diffusion processes
The limit behavior of the number of crossings of some sequence of levels by the following sequence of random variables ξ_n(0), ξ_n(1m), …, ξ_n(Nm), as the integers n, m, N are increasing to infinity in some consistent way, is investigated, where (ξ_n(t))_t0 for n=1,2,… is a diffusion process on a real line R with its local characteristics (that is, drift and diffusion coefficients) (a_n(x))_xR and (b_n(x))_xR given by a_n(x)=na(nx), b_n(x)=b(nx) for xR and n=1,2,… with some fixed functions (a(x))_xR and (b(x))_xR . , number=2, journal=Carpathian Mathematical Publications, author=Osypchuk, M.M., year=2009, month=Dec., pages=191–196