Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields
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| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-4250-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4250-4 | ||
| 245 | 0 | 0 | |a Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields |h [Elektronische Daten] |c [Zhen Chen, Quan Zhou] |
| 520 | 3 | |a 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. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Anisotropic random field |2 nationallicence | |
| 690 | 7 | |a non-linear stochastic heat equations |2 nationallicence | |
| 690 | 7 | |a spatially homogeneous Gaussian noise |2 nationallicence | |
| 690 | 7 | |a hitting probabilities |2 nationallicence | |
| 690 | 7 | |a Hausdorff dimension |2 nationallicence | |
| 690 | 7 | |a inverse image |2 nationallicence | |
| 700 | 1 | |a Chen |D Zhen |u School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China |4 aut | |
| 700 | 1 | |a Zhou |D Quan |u School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/12(2015-12-01), 1895-1922 |x 1439-8516 |q 31:12<1895 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4250-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4250-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chen |D Zhen |u School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhou |D Quan |u School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/12(2015-12-01), 1895-1922 |x 1439-8516 |q 31:12<1895 |1 2015 |2 31 |o 10114 | ||