[1] Khoshnevisan D. Intersections of Brownian motions. Expos Math, 2003, 21:97-114 [2] Taylor S J. The measure theory of random fractals. Math Proc Cambridge Philo Soc, 1986, 100:383-406 [3] Rosen J. The intersection local time of fractional Brownian motion in the plane. J Multivar Anal, 1987, 23:37-46 [4] Kahane J P. Some Random Series of Functions. London:Cambridge University Press, 1985 [5] Evans S N. Potential theory for a family of several Markov processes. Ann Inst H Poincaré Probab Statist, 1987, 23:499-530 [6] Tongring N. Which sets contain multiple points of Brownian motion? Math Proc Cambridge Philo Soc, 1988, 103:181-187 [7] Fitzsimmons P J, Salisbury T S. Capacity and energy for multiparameter processes. Ann Inst H Poincaré Probab Statist, 1989, 25:325-350 [8] Peres Y. Probability on trees:an introductory climb Lectures on Probability Theory and Statistics (SaintFlour)//Lecture Notes in Math. Berlin Heidelberg:Springer, 1999, 1717:193-280 [9] Chen Z. Fractal properties of polar sets of random string processes. Acta Math Sci, 2011, 31B(3):969-992 [10] Dalang R C, Khoshnevisan D, Nualart E, et al. Critical Brownian sheet does not have double points. Ann Probab, 2012, 40:1829-1859 [11] Chen Z, Xiao Y. On intersections of independent anisotropic Gaussian random fields. Sci China Math, 2012, 55:2217-2232 [12] Chen Z, Wang J, Wu D. On intersections of independent space-time anisotropic Gaussian fields. Statist Probab Lett, 2020, 166:108874 [13] Dalang R C, Khoshnevisan D, Nualart E. Hitting probabilities for systems of non-linear stochastic heat equations with additive noise. ALEA Latin Amer J Probab Statist, 2007, 3:231-271 [14] Dalang R C, Khoshnevisan D, Nualart E. Hitting probabilities for the non-linear stochastic heat equation with multiplicative noise. Probab Theory Rel Fields, 2009, 144:371-427 [15] Dalang R C, Khoshnevisan D, Nualart E. Hitting probabilities for systems of non-linear stochastic heat equations in spatial dimensions k ≥ 1. Stoch PDE:Anal Comp, 2013, 1:94-151 [16] Dalang R C, Pu F. Optimal lower bounds on hitting probabilites for non-linear systems of stochastic fractional heat equations. Stochastic Process Appl, 2021, 131:359-393 [17] Dalang R C, Sanz-Solé M. Criteria for hitting probabilities with applications to systems of stochastic wave equations. Bernoulli, 2010, 16:1343-1368 [18] Chen Z. Multiple intersections of independent random fields and Hausdorff dimension(in Chinese). Sci China Math, 2016, 46:1279-1304 [19] Ouyang C, Shi Y, Wu D. Mutual intersection for rough differential systems driven by fractional Brownian motions. Statist Probab Lett, 2018, 135:83-91 [20] Kamont A. On the fractional anisotropic Wiener field. Probab Math Statist, 1996, 16:85-98 [21] Chen Z. Intersections and polar functions of fractional Brownian sheets. Acta Math Sci, 2008, 28B(4):779-796 [22] Mueller C, Tribe R. Hitting probabilities of a random string. Electron J Probab, 2002, 7(10):1-29 [23] Xiao Y. Sample path properties of anisotropic Gaussian random fields//Khoshnevisan D, Rassoul-Agha F. A Minicourse on Stochastic Partial Differential Equations. Lecture Notes in Mathematics. New York:Springer, 2009, 1962:145-212 [24] Wu D, Xiao Y. Uniform dimension results for Gaussian random fields. Sci China Ser A, 2009, 52:1478-1496 [25] Adler R J. The Geometry of Random Fields. New York:Wiley, 1981 [26] Xiao Y. Dimension results for Gaussian vector fields and index-α stable fields. Ann Probab, 1995, 23:273-291 [27] Xiao Y. Hausdorff dimension of the graph of fractional Brownian motion. Math Proc Cambridge Philo Soc, 1997, 122:565-576 [28] Didier G, Pipiras V. Integral representations of operator fractional Brownian motions. Bernoulli, 2011, 17:1-33 [29] Mason D J, Xiao Y. Sample path properties of operator self-similar Gaussian random fields. Theor Probab Appl, 2002, 46:58-78 [30] Li Y, Xiao Y. Multivariate operator-self-similar random fields. Stoch Process Appl, 2011, 121:1178-1200 [31] Ni W, Chen Z. Hitting probabilities and dimension results for space-time anisotropic Gaussian fields (in Chinese). Sci China Math, 2018, 48:419-442 [32] Ni W, Chen Z. Hausdorff measure of the range of space-time anisotropic Gaussian random fields. J Theoret Probab, 2021, 34:264-282 [33] Xiao Y. Recenct developments on fractal properties of Gaussian random fields//Barral J, Seuret S. Further Developments in Fractals and Related Fields. New York:Springer, 2013:255-288 [34] Biermé H, Lacaux C, Xiao Y. Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields. Bull Lond Math Soc, 2009, 41:253-273 [35] Wu D. On the solution process for a stochastic fractional partial differential equation driven by space-time white noise. Statist Probab Lett, 2011, 81(8):1161-1172 [36] Chen Z, Zhou Q. Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields. Acta Math Sin (Engl Ser), 2015, 31(12):1895-1922 [37] Chen Z. On intersections of independent nondegenerate diffusion processes. Acta Math Sci, 2014, 34B(1):141-161 [38] Kwaśnicki M. Ten equivalent definitions of the fractional Laplace operator. Fract Calc Appl Anal, 2017, 20(1):7-51 [39] Walsh J B. An introduction to stochastic partial differential equations//Ecole d'Eté de Probabilités de Saint-Flour XIV; Lect Notes in Math. Berlin Heidelberg:Springer, 1986, 1180:266-437 |