Large Deviations and Laws of the Iterated Logarithm for the Local times of Additive Stable Processes
نویسنده
چکیده
We study the upper tail behaviors of the local times of the additive stable processes. Let X1(t), · · · , Xp(t) be independent, d-dimensional symmetric stable processes with stable index 0 < α ≤ 2 and consider the additive stable process X(t1, · · · , tp) = X1(t1) + · · · + Xp(tp). Under the condition d < αp, we obtain a precise form of large deviation principle for the local time
منابع مشابه
Moderate Deviations and Laws of the Iterated Logarithm for the Local times of Additive Lévy Processes and Additive Random Walks
We study the upper tail behaviors of the local times of the additive Lévy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L2-norms of the local times and for the local times at a fixed site. Subject classifications: 60F10, 60F15, 60J55, 60G52
متن کاملModerate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times
متن کاملLaws of the Iterated Logarithm for Symmetric Jump Processes
Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.
متن کاملLarge deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes
In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...
متن کاملLaws of the Iterated Logarithm for a Class of Iterated Processes
Let X = {X(t), t ≥ 0} be a Brownian motion or a spectrally negative stable process of index 1 < α < 2. Let E = {E(t), t ≥ 0} be the hitting time of a stable subordinator of index 0 < β < 1 independent of X . We use a connection between X(E(t)) and the stable subordinator of index β/α to derive information on the path behavior of X(Et). This is an extension of the connection of iterated Brownian...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006