Convergence Criteria for Multiparameter Stochastic Processes and Some Applications, The Annals of Mathematical Statistics, vol.42, issue.5, pp.1656-1670, 1971. ,
DOI : 10.1214/aoms/1177693164
URL : http://doi.org/10.1214/aoms/1177693164
Invariance principles for self-similar set-indexed random fields, Transactions of the American Mathematical Society, vol.366, issue.11, pp.5963-5989, 2014. ,
DOI : 10.1090/S0002-9947-2014-06135-7
Invariance principles for operator-scaling Gaussian random fields, The Annals of Applied Probability, vol.27, issue.2, pp.1190-1234, 2017. ,
DOI : 10.1214/16-AAP1229
Operator scaling stable random fields. Stochastic Process, Appl, vol.117, issue.3, pp.312-332, 2007. ,
Convergence of probability measures Wiley Series in Probability and Statistics: Probability and Statistics, 1999. ,
Regular variation, volume 27 of Encyclopedia of Mathematics and its Applications, 1987. ,
From infinite urn schemes to decompositions of self-similar Gaussian process, Electron. J. Probab, vol.21, issue.23, 2016. ,
A simple construction of the fractional Brownian motion. Stochastic Process, Appl, vol.109, issue.2, pp.203-223, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00101987
Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws, Probability Surveys, vol.4, issue.0, pp.146-171, 2007. ,
DOI : 10.1214/07-PS092
Power law Pólya's urn and fractional Brownian motion. Probab. Theory Related Fields, pp.3-4691, 2013. ,
DOI : 10.1007/s00440-012-0468-6
URL : http://arxiv.org/pdf/0903.1284
Stochastic partial differential equations driven by multiparameter fractional white noise, Stochastic processes, physics and geometry: new interplays, II (Leipzig CMS Conf. Proc, pp.327-337, 1999. ,
Foundations of modern probability. Probability and its Applications, 1997. ,
On the fractional anisotropic Wiener field, Probab. Math. Statist, vol.16, issue.1, pp.85-98, 1996. ,
Central Limit Theorems for Certain Infinite Urn Schemes, Indiana University Mathematics Journal, vol.17, issue.4, pp.373-401, 1967. ,
DOI : 10.1512/iumj.1968.17.17020
URL : http://doi.org/10.1512/iumj.1968.17.17020
Fractional Brownian motion as a weak limit of Poisson shot noise processes?with applications to finance. Stochastic Process, Appl, vol.113, issue.2, pp.333-351, 2004. ,
Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.), vol.26, pp.115-118, 1940. ,
Invariance principles for non-isotropic long memory random fields, Statistical Inference for Stochastic Processes, vol.16, issue.3, pp.255-282, 2007. ,
DOI : 10.1007/s11203-006-9001-9
Aggregation of isotropic autoregressive fields [corrigendum to mr2523650], J. Statist. Plann. Inference, issue.12, pp.1413862-3866, 2011. ,
A decomposition of the bifractional Brownian motion and some applications, Statistics & Probability Letters, vol.79, issue.5, pp.619-624, 2009. ,
DOI : 10.1016/j.spl.2008.10.009
Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review, vol.10, issue.4, pp.422-437, 1968. ,
DOI : 10.1137/1010093
Dependent Central Limit Theorems and Invariance Principles, The Annals of Probability, vol.2, issue.4, pp.620-628, 1974. ,
DOI : 10.1214/aop/1176996608
Scaling Limits for Cumulative Input Processes, Mathematics of Operations Research, vol.32, issue.4, pp.890-918, 2007. ,
DOI : 10.1287/moor.1070.0267
URL : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.225.5660&rep=rep1&type=pdf
Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations, Stochastics and Stochastic Reports, vol.1180, issue.3-4, pp.3-4141, 2001. ,
DOI : 10.1007/BFb0074920
On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion, ALEA Lat. Am. J. Probab. Math. Stat, vol.4, pp.245-255, 2008. ,
Long-range dependence and self-similarity, 2015. ,
DOI : 10.1017/CBO9781139600347
Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics, Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, 2002. ,
Scaling transition for long-range dependent Gaussian random fields. Stochastic Process, Appl, vol.125, issue.6, pp.2256-2271, 2015. ,
Aggregation of autoregressive random fields and anisotropic long-range dependence, Bernoulli, vol.22, issue.4, pp.2401-2441, 2016. ,
DOI : 10.3150/15-BEJ733
Stochastic processes and long range dependence. Springer Series in Operations Research and Financial Engineering, 2016. ,
DOI : 10.1007/978-3-319-45575-4
An Invariance Principle for Fractional Brownian Sheets, Journal of Theoretical Probability, vol.32, issue.2, pp.1124-1139, 2014. ,
DOI : 10.1007/978-3-540-85994-9_5
URL : http://arxiv.org/pdf/1109.5160
Sample Path Properties of Anisotropic Gaussian Random Fields, A minicourse on stochastic partial differential equations, pp.145-212, 2009. ,
DOI : 10.1007/978-3-540-85994-9_5
E-mail address: yizao.wang@uc, pp.45221-45246 ,