کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7549939 1489920 2018 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Extremes of q-Ornstein-Uhlenbeck processes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Extremes of q-Ornstein-Uhlenbeck processes
چکیده انگلیسی
Two limit theorems are established on the extremes of a family of stationary Markov processes, known as q-Ornstein-Uhlenbeck processes with q∈(−1,1). Both results are crucially based on the weak convergence of the tangent process at the lower boundary of the domain of the process, a positive self-similar Markov process little investigated so far in the literature. The first result is the asymptotic excursion probability established by the double-sum method, with an explicit formula for the Pickands constant in this context. The second result is a Brown-Resnick-type limit theorem on the minimum process of i.i.d. copies of the q-Ornstein-Uhlenbeck process: with appropriate scalings in both time and magnitude, a new semi-min-stable process arises in the limit.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 128, Issue 9, September 2018, Pages 2979-3005
نویسندگان
,