caa a22 4500 605461422 CHVBK 20210128100243.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10114-015-4250-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4250-4 Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields [Elektronische Daten] [Zhen Chen, Quan Zhou] Let X = {X(t): t ∈ R N } be an anisotropic random field with values in R d . Under certain conditions on X, we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity. We also obtain the Hausdorff dimension of its inverse image, and the Hausdorff and packing dimensions of its level sets. These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Anisotropic random field nationallicence non-linear stochastic heat equations nationallicence spatially homogeneous Gaussian noise nationallicence hitting probabilities nationallicence Hausdorff dimension nationallicence inverse image nationallicence Chen Zhen School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China aut Zhou Quan School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1895-1922 1439-8516 31:12<1895 2015 31 10114 https://doi.org/10.1007/s10114-015-4250-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4250-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Zhen School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China aut NATIONALLICENCE 700 1- Zhou Quan School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1895-1922 1439-8516 31:12<1895 2015 31 10114