Cong, Tianshu; Xia, Aihua Normal approximation in total variation for statistics in geometric probability. (English) Zbl 07807056 Adv. Appl. Probab. 56, No. 1, 106-155 (2024). Reviewer: Pavel Stoynov (Sofia) MSC: 60F05 60D05 60G55 62E20 PDFBibTeX XMLCite \textit{T. Cong} and \textit{A. Xia}, Adv. Appl. Probab. 56, No. 1, 106--155 (2024; Zbl 07807056) Full Text: DOI arXiv
Cong, Tianshu; Xia, Aihua Convergence rate for geometric statistics of point processes having fast decay of dependence. (English) Zbl 1521.60012 Electron. J. Probab. 28, Paper No. 90, 35 p. (2023). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60F05 60D05 60G55 62E20 05C80 PDFBibTeX XMLCite \textit{T. Cong} and \textit{A. Xia}, Electron. J. Probab. 28, Paper No. 90, 35 p. (2023; Zbl 1521.60012) Full Text: DOI arXiv
Chen, Louis H. Y.; Röllin, Adrian; Xia, Aihua Palm theory, random measures and Stein couplings. (English) Zbl 1484.60025 Ann. Appl. Probab. 31, No. 6, 2881-2923 (2021). Reviewer: Fraser Daly (Edinburgh) MSC: 60F05 60G55 60G57 60D05 62E17 PDFBibTeX XMLCite \textit{L. H. Y. Chen} et al., Ann. Appl. Probab. 31, No. 6, 2881--2923 (2021; Zbl 1484.60025) Full Text: DOI arXiv
Cong, Tianshu; Xia, Aihua; Zhang, Fuxi A large sample property in approximating the superposition of i.i.d. finite point processes. (English) Zbl 1434.60067 Stochastic Processes Appl. 130, No. 7, 4493-4511 (2020). MSC: 60F05 60E15 60G55 PDFBibTeX XMLCite \textit{T. Cong} et al., Stochastic Processes Appl. 130, No. 7, 4493--4511 (2020; Zbl 1434.60067) Full Text: DOI arXiv
Barbour, A. D.; Xia, A. Multivariate approximation in total variation using local dependence. (English) Zbl 1467.60018 Electron. J. Probab. 24, Paper No. 27, 35 p. (2019). MSC: 60F05 60E15 60G55 60J27 PDFBibTeX XMLCite \textit{A. D. Barbour} and \textit{A. Xia}, Electron. J. Probab. 24, Paper No. 27, 35 p. (2019; Zbl 1467.60018) Full Text: DOI arXiv Euclid
Keeler, H. Paul; Ross, Nathan; Xia, Aihua When do wireless network signals appear Poisson? (English) Zbl 1429.60049 Bernoulli 24, No. 3, 1973-1994 (2018). MSC: 60G55 60B10 94A17 PDFBibTeX XMLCite \textit{H. P. Keeler} et al., Bernoulli 24, No. 3, 1973--1994 (2018; Zbl 1429.60049) Full Text: DOI arXiv Euclid
Keeler, Paul; Ross, Nathan; Xia, Aihua; Blaszczyszyn, Bartlomiej Stronger wireless signals appear more Poisson. arXiv:1604.02986 Preprint, arXiv:1604.02986 [cs.NI] (2016). MSC: 60G55 BibTeX Cite \textit{P. Keeler} et al., ``Stronger wireless signals appear more Poisson'', Preprint, arXiv:1604.02986 [cs.NI] (2016) Full Text: DOI arXiv OA License
Xia, Aihua; Yukich, J. E. Normal approximation for statistics of Gibbsian input in geometric probability. (English) Zbl 1333.60037 Adv. Appl. Probab. 47, No. 4, 934-972 (2015). MSC: 60F05 60G55 60D05 05C80 91B30 PDFBibTeX XMLCite \textit{A. Xia} and \textit{J. E. Yukich}, Adv. Appl. Probab. 47, No. 4, 934--972 (2015; Zbl 1333.60037) Full Text: DOI arXiv Euclid
Gan, H. L.; Xia, A. Stein’s method for conditional compound Poisson approximation. (English) Zbl 1327.60059 Stat. Probab. Lett. 100, 19-26 (2015). MSC: 60F05 60G55 60E15 60G70 60J27 PDFBibTeX XMLCite \textit{H. L. Gan} and \textit{A. Xia}, Stat. Probab. Lett. 100, 19--26 (2015; Zbl 1327.60059) Full Text: DOI
Xia, Aihua; Zhang, Fuxi On the asymptotics of locally dependent point processes. (English) Zbl 1247.60069 Stochastic Processes Appl. 122, No. 9, 3033-3065 (2012). MSC: 60G55 60F05 60E15 PDFBibTeX XMLCite \textit{A. Xia} and \textit{F. Zhang}, Stochastic Processes Appl. 122, No. 9, 3033--3065 (2012; Zbl 1247.60069) Full Text: DOI
Novak, S. Y.; Xia, A. On exceedances of high levels. (English) Zbl 1234.60059 Stochastic Processes Appl. 122, No. 2, 582-599 (2012). MSC: 60G70 60G55 60E15 60F05 PDFBibTeX XMLCite \textit{S. Y. Novak} and \textit{A. Xia}, Stochastic Processes Appl. 122, No. 2, 582--599 (2012; Zbl 1234.60059) Full Text: DOI
Chen, Louis H. Y.; Xia, Aihua Poisson process approximation for dependent superposition of point processes. (English) Zbl 1248.60054 Bernoulli 17, No. 2, 530-544 (2011). MSC: 60G55 60F05 60K05 PDFBibTeX XMLCite \textit{L. H. Y. Chen} and \textit{A. Xia}, Bernoulli 17, No. 2, 530--544 (2011; Zbl 1248.60054) Full Text: DOI arXiv Euclid
Xia, Aihua; Zhang, Fuxi Stein’s method and locally dependent point process approximation. arXiv:1102.4153 Preprint, arXiv:1102.4153 [math.PR] (2011). MSC: 60G55 60E15 BibTeX Cite \textit{A. Xia} and \textit{F. Zhang}, ``Stein's method and locally dependent point process approximation'', Preprint, arXiv:1102.4153 [math.PR] (2011) Full Text: arXiv OA License
Tan, Sen; Xia, Aihua On customer flows in Jackson queueing networks. (English) Zbl 1218.60083 Adv. Appl. Probab. 42, No. 4, 1094-1101 (2010). Reviewer: Jerzy Martyna (Kraków) MSC: 60K25 90B22 60E15 60F05 60G55 PDFBibTeX XMLCite \textit{S. Tan} and \textit{A. Xia}, Adv. Appl. Probab. 42, No. 4, 1094--1101 (2010; Zbl 1218.60083) Full Text: DOI arXiv
Schuhmacher, Dominic; Xia, Aihua A new metric between distributions of point processes. (English) Zbl 1155.60020 Adv. Appl. Probab. 40, No. 3, 651-672 (2008). Reviewer: Viktor Oganyan (Erevan) MSC: 60G55 60F05 62M30 PDFBibTeX XMLCite \textit{D. Schuhmacher} and \textit{A. Xia}, Adv. Appl. Probab. 40, No. 3, 651--672 (2008; Zbl 1155.60020) Full Text: DOI arXiv
Xia, Aihua; Zhang, Fuxi A polynomial birth-death point process approximation to the Bernoulli process. (English) Zbl 1147.60020 Stochastic Processes Appl. 118, No. 7, 1254-1263 (2008). MSC: 60F05 60G55 60J80 PDFBibTeX XMLCite \textit{A. Xia} and \textit{F. Zhang}, Stochastic Processes Appl. 118, No. 7, 1254--1263 (2008; Zbl 1147.60020) Full Text: DOI
Chen, Louis H. Y.; Xia, Aihua Poisson process approximation: from Palm theory to Stein’s method. (English) Zbl 1268.60064 Ho, Hwai-Chung (ed.) et al., Time series and related topics. In memory of Ching-Zong Wei. Selected papers based on the presentations at the conference, Taipei, Taiwan, December 12–14, 2005. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-68-3/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 52, 236-244 (2006). MSC: 60G55 60F05 PDFBibTeX XMLCite \textit{L. H. Y. Chen} and \textit{A. Xia}, IMS Lect. Notes, Monogr. Ser. 52, 236--244 (2006; Zbl 1268.60064) Full Text: arXiv
Chen, Louis H. Y.; Xia, Aihua Stein’s method, Palm theory and Poisson process approximation. (English) Zbl 1057.60051 Ann. Probab. 32, No. 3B, 2545-2569 (2004). Reviewer: Laura L. Ramos (São Paulo) MSC: 60G55 60E05 60E15 PDFBibTeX XMLCite \textit{L. H. Y. Chen} and \textit{A. Xia}, Ann. Probab. 32, No. 3B, 2545--2569 (2004; Zbl 1057.60051) Full Text: DOI arXiv
Xia, Aihua Point processes characterized by their one dimensional distributions. (English) Zbl 1042.60029 Probab. Theory Relat. Fields 128, No. 3, 467-474 (2004). MSC: 60G55 60E05 60B10 PDFBibTeX XMLCite \textit{A. Xia}, Probab. Theory Relat. Fields 128, No. 3, 467--474 (2004; Zbl 1042.60029) Full Text: DOI
Brown, Timothy C.; Xia, Aihua How many processes have Poisson counts? (English) Zbl 1059.60064 Stochastic Processes Appl. 98, No. 2, 331-339 (2002). MSC: 60G55 60G07 PDFBibTeX XMLCite \textit{T. C. Brown} and \textit{A. Xia}, Stochastic Processes Appl. 98, No. 2, 331--339 (2002; Zbl 1059.60064) Full Text: DOI
Barbour, A. D.; Novak, S. Y.; Xia, A. Compound Poisson approximation for the distribution of extremes. (English) Zbl 1005.60065 Adv. Appl. Probab. 34, No. 1, 223-240 (2002). Reviewer: Wiesław Dziubdziela (Kielce) MSC: 60G70 60F05 60G55 PDFBibTeX XMLCite \textit{A. D. Barbour} et al., Adv. Appl. Probab. 34, No. 1, 223--240 (2002; Zbl 1005.60065) Full Text: DOI
Brown, Timothy C.; Xia, Aihua Stein’s method and birth-death processes. (English) Zbl 1019.60019 Ann. Probab. 29, No. 3, 1373-1403 (2001). Reviewer: A.D.Barbour (Zürich) MSC: 60F05 60E15 60E05 60J80 PDFBibTeX XMLCite \textit{T. C. Brown} and \textit{A. Xia}, Ann. Probab. 29, No. 3, 1373--1403 (2001; Zbl 1019.60019) Full Text: DOI
Brown, Timothy C.; Weinberg, Graham V.; Xia, Aihua Removing logarithms from Poisson process error bounds. (English) Zbl 1045.60045 Stochastic Processes Appl. 87, No. 1, 149-165 (2000). Reviewer: Martin Janžura (Praha) MSC: 60G55 60K25 PDFBibTeX XMLCite \textit{T. C. Brown} et al., Stochastic Processes Appl. 87, No. 1, 149--165 (2000; Zbl 1045.60045) Full Text: DOI
Xia, Aihua Poisson approximation, compensators and coupling. (English) Zbl 0953.60031 Stochastic Anal. Appl. 18, No. 1, 159-177 (2000). MSC: 60G55 60G44 PDFBibTeX XMLCite \textit{A. Xia}, Stochastic Anal. Appl. 18, No. 1, 159--177 (2000; Zbl 0953.60031) Full Text: DOI
Barbour, A. D.; Brown, Timothy C.; Xia, Aihua Point processes in time and Stein’s method. (English) Zbl 0924.60020 Stochastics Stochastics Rep. 65, No. 1-2, 127-151 (1998). Reviewer: V.Oganyan (Erevan) MSC: 60G55 PDFBibTeX XMLCite \textit{A. D. Barbour} et al., Stochastics Stochastics Rep. 65, No. 1--2, 127--151 (1998; Zbl 0924.60020) Full Text: DOI
Brown, Timothy C.; Hamza, Kais; Xia, Aihua On the variance to mean ratio for random variables from Markov chains and point processes. (English) Zbl 0942.60003 J. Appl. Probab. 35, No. 2, 303-312 (1998). Reviewer: V.Thangaraj (Madras) MSC: 60E15 60J27 60G55 PDFBibTeX XMLCite \textit{T. C. Brown} et al., J. Appl. Probab. 35, No. 2, 303--312 (1998; Zbl 0942.60003) Full Text: DOI
He, S.; Xia, A. On Poisson approximation to the partial sum process of a Markov chain. (English) Zbl 0889.60049 Stochastic Processes Appl. 68, No. 1, 101-111 (1997). MSC: 60G55 60E15 PDFBibTeX XMLCite \textit{S. He} and \textit{A. Xia}, Stochastic Processes Appl. 68, No. 1, 101--111 (1997; Zbl 0889.60049) Full Text: DOI
Xia, Aihua On using the first difference in the Stein-Chen method. (English) Zbl 0903.60012 Ann. Appl. Probab. 7, No. 4, 899-916 (1997). Reviewer: A.D.Barbour (Zürich) MSC: 60E15 62E17 60G55 PDFBibTeX XMLCite \textit{A. Xia}, Ann. Appl. Probab. 7, No. 4, 899--916 (1997; Zbl 0903.60012) Full Text: DOI
Xia, Aihua On the rate of Poisson process approximation to a Bernoulli process. (English) Zbl 0920.60026 J. Appl. Probab. 34, No. 4, 898-907 (1997). Reviewer: Valeriy Koval’ (Shytomyr) MSC: 60G55 60E15 PDFBibTeX XMLCite \textit{A. Xia}, J. Appl. Probab. 34, No. 4, 898--907 (1997; Zbl 0920.60026) Full Text: DOI
Brown, Timothy C.; Xia, Aihua On metrics in point process approximation. (English) Zbl 0864.60035 Stochastics Stochastics Rep. 52, No. 3-4, 247-263 (1995). MSC: 60G55 PDFBibTeX XMLCite \textit{T. C. Brown} and \textit{A. Xia}, Stochastics Stochastics Rep. 52, No. 3--4, 247--263 (1995; Zbl 0864.60035) Full Text: DOI
Xia, Aihua A note on the Prohorov distance between a counting process and a Poisson process. (English) Zbl 0810.60043 Stochastics Stochastics Rep. 45, No. 1-2, 61-77 (1993). Reviewer: B.P.Harlamov (St.Peterburg) MSC: 60G55 PDFBibTeX XMLCite \textit{A. Xia}, Stochastics Stochastics Rep. 45, No. 1--2, 61--77 (1993; Zbl 0810.60043) Full Text: DOI