The Localization Phenomenon For Occupation Time Of Brownian Sheet And Its Applications

The multifractal analysis of random process has been paid close attention by many scholars in the last few years alone with a series of papers about the multifractal decompsition of the occupation time of Brownian motion published by Peres and Zeitouni etc. on famous publication Acta Math etc. The so-called " the localization phenomenon of occupation time " of transient Brownian motion (d > 3) played an key role in solving the problem about the Hausdorff dimension and Packing dimension of the so-called " thick point" sets, as well as asymptotic laws for the whole occupation time of Brownian motion. " The localization phenomenon of occupation time " breaks down in d = 2 dimension Brownian motion . However, it is unknowed that whether Brownian sheet ,which also has recurrent property, enjoies the localization phenomenon of occupation time .In the paper, we discuss the localization phenomenon of occupation time for transient (d > 2N)Brownain sheet. Because of the partially-ordered nature in the muti-parameter index space and the distinctness between Brownian motion and Brownian sheet, we can't determine the accurate constants as well as Brownian motion's. We obtain the localization phenomenon of occupation time for transient Brownain sheet and its applications in asymptotic laws and mutltifractal decomposition as follow:Let W = {W{s) : s G [0, )N} be N-parameter Brownian sheet in Rd,d > 2N,(I) for some 0 < c < oo, sufficiently small ε0 >0, and all 0 < ε < εo, t where is the first positive zero of the Bessel founction Jd/2-2.(II) 1) for some where...