کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155931 958785 2011 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Estimates for the probability that Itô processes remain near a path
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Estimates for the probability that Itô processes remain near a path
چکیده انگلیسی

Let W=(Wi)i∈NW=(Wi)i∈N be an infinite dimensional Brownian motion and (Xt)t≥0(Xt)t≥0 a continuous adaptednn-dimensional process. Set τR=inf{t:|Xt−xt|≥Rt}τR=inf{t:|Xt−xt|≥Rt}, where xt,t≥0xt,t≥0 is a RnRn-valued deterministic differentiable curve and Rt>0,t≥0Rt>0,t≥0 a time-dependent radius. We assume that, up to τRτR, the process XX solves the following (not necessarily Markov) SDESDE:Xt∧τR=x+∑j=1∞∫0t∧τRσj(s,ω,Xs)dWsj+∫0t∧τRb(s,ω,Xs)ds. Under local conditions on the coefficients, we obtain lower bounds for P(τR≥T)P(τR≥T) as well as estimates for distribution functions and expectations. These results are discussed in the elliptic and log-normal frameworks. An example of a diffusion process that satisfies the weak Hörmander condition is also given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 121, Issue 9, September 2011, Pages 2087–2113
نویسندگان
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