Quasi sure functional modulus of continuity for a two-parameter Wiener process in Hölder norm

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• 作者：Jie Xu ^{xujiescu@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Schilder's theorem ; Large deviations ; Two-parameter Wiener process ; Cr ; pCr ; p-capacity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：501-515
• 全文大小：340 K

文摘

In this paper, we establish a large deviation principle for increments of a two-parameter Wiener process in Hölder norm with respect to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15007489&_mathId=si1.gif&_user=111111111&_pii=S0022247X15007489&_rdoc=1&_issn=0022247X&md5=00924ba75194f752cd72cbde06113c92" title="Click to view the MathML source">C_r,pclass="mathContainer hidden">class="mathCode">$C_{r,p}$-capacity on an abstract Wiener space. Moreover, a quasi sure functional modulus of continuity for a two-parameter Wiener process in Hölder norm is also derived.