Aihua Xia
School of Mathematics and Statistics
The University of Melbourne
Vic 3010, Australia.
Email: aihuaxia@unimelb.edu.au
Phone: +6138344 4247
Fax: +6138344 4599
My name
The given name is pronounced as "eihwa:" ("Ai"="a" in abc, "h"="h" in hurry, "u" ="w" in "wait",
while the final "a" is approximately equal to "ah" as in blah).
My surname can be roughly pronounced as shar, shark without k.
Research interests
 Point processes
 Limit theory of random processes
 Applied probability and Stein's method
 Markov processes
 Queueing Networks
 Image Processing
Academic vitae
Selected publications

“Multivariate approximation in total variation using local dependence
” (with A.D. Barbour).
Electronic Journal of Probability 24
(2019), paper no. 27, 135.

“Divergence from, and Convergence to, Uniformity of Probability Density
Quantiles” (with R. G. Staudte).
Entropy 20 (5)
(2018), article 317, 110.

“Multivariate approximation in total variation, I: equilibrium distributions of Markov jump
processes” (with A.D. Barbour and M. J. Luczak).
Annals of Probability 46
(2018), 13511404.

“Multivariate approximation in total variation, II: discrete normal
approximation” (with A.D. Barbour and M. J. Luczak).
Annals of Probability 46
(2018), 14051440.

“When do wireless network signals appear
Poisson?” (with H. P. Keeler and N. Ross).
Bernoulli, 24
(2018), 19731994.

“Normal approximation for statistics of Gibbsian input in geometric
probability” (with J. E. Yukich).
Adv. Appl. Prob., 47
(2015), 139.

“Stein's method for conditional compound Poisson
approximation” (with H. L. Gan).
Statistics and Probability Letters,
100
(2015), 1926.

“Stein factors for negative binomial approximation in Wasserstein
distance” (with A. D. Barbour, H. L. Gan).
Bernoulli,
21
(2015), 10021013.

“On asymptotics of locally dependent point
processes” (with F. Zhang).
Stochastic Processes and their Applications,
122
(2012), 30333065.

“On exceedances of high
levels” (with S. Novak).
Stochastic Processes and their Applications,
122
(2012), 582599.

“Clubbed Binomial Approximation for the Lightbulb
Process” (with L. Goldstein).
Probability Approximations and Beyond, Lecture Notes in Statistics,
205
(2012), 3141.

“Changing Topological Patterns in Normal Ageing Using Largescale Structural
Networks” (with W. Zhu, W. Wen, Y. He, K. J. Anstey, P. Sachdev).
Neurobiology of Aging,
33
(2012), 899913.

“Discrete neuroanatomical networks are associated with specific cognitive abilities in old
age” (with W. Wen, W. Zhu, Y. He, N. Kochan, S. Reppermund, M. Slavin, H. Brodaty, J. Crawford and P. Sachdev).
Journal of Neuroscience,
31
(2011), 12041212.

“The Wasted Vote Phenomenon with Uncertain Voter
Population” (with Y. L. Chen).
Social Choice and Welfare,
37
(2011), 471492.

“Poisson process approximation for dependent superposition of point
processes” (with L. H. Y. Chen).
Bernoulli,
17
(2011), 530544.

“On customer flows in Jackson queuing
networks” (with S. Tan).
Advances in Applied Probability,
42
(2010),
10941101.

“On approximation of Markov binomial
distributions” (with M. Zhang).
Bernoulli,
15
(2009),
13351350.

“Polynomial birthdeath distribution approximation in Wasserstein
distance” (with F. Zhang).
Journal of Theoretical Probability,
22
(2009),
294310.

“A new metric between distributions of point
processes” (with D. Schuhmacher).
Advances in Applied Probability,
40
(2008),
651672.

“On negative binomial approximation to
$k$runs” (with X. Wang).
Journal of Applied Probability,
45
(2008),
456471.

“A polynomial birthdeath point process approximation to the Bernoulli
process” (with F. Zhang).
Stochastic Processes and their Applications,
118
(2008),
12541263.

“On Stein's method and
perturbations” (with A. D. Barbour and V. Cekanavicius).
Latin American Journal Of Probability And Mathematical Statistics,
3
(2007),
3153.

“Normal approximation for random
sums” (with A. D. Barbour).
Advances in Applied Probability,
38
(2006),
693728.

“On Stein's factors for Poisson approximation in Wasserstein
distance” (with A. D. Barbour).
Bernoulli,
12
(2006),
943954..

“Zero Biasing and a Discrete Central Limit
Theorem” (with L. Goldstein).
Annals of Probability,
34
(2006),
17821806.

“Stein's method and Poisson process
approximation”.
An Introduction to Stein's Method, Eds. A. D. Barbour and L. H. Y. Chen,
World Scientific
Press,
(2005),
115181.

“Stein's method for compound Poisson approximation
via immigrationdeath processes”.
Stein's Method and Applications,
Eds. A. D. Barbour and L. H. Y. Chen, World Scientific
Press
(2005),
85102.

“Nonrandom Clusters of Palindromes in Herpesvirus
Genomes” (with M. Y. Leung, K. P. Choi and L. H. Y. Chen).
Journal of Computational Biology,
12
(2005),
331354.

“Stein's method, Palm theory and Poisson process
approximation” (with L. H. Y. Chen).
Annals of Probability,
32
(2004),
25452569.

“Point processes characterized by their one dimensional distributions”.
Probab. Theory Related Fields,
128 (2004),
467474.

“How many processes have Poisson counts?” (with T. C. Brown).
Stochastic Processes and their
Applications,
98
(2002),
331339.

“Compound Poisson approximation for the distribution of extremes”
(with A. D. Barbour and
S. Y. Novak).
Advances in Applied Probability,
34
(2002),
223240.

“Stein's method and birthdeath processes” (with T. C. Brown).
Annals of Probability,
29
(2001),
13731403.

“The number of two dimensional maxima” (with A. D. Barbour).
Advances in Applied Probability,
33
(2001),
727750.

“Removing Logarithms from Poisson Process Error Bounds”
(with T. C. Brown and G. V. Weinberg).
Stochastic processes and their applications,
87
(2000),
149165.

“Estimating Stein's constants for
compound Poisson approximation” (with A. D. Barbour).
Bernoulli,
6
(2000),
581590.

“Poisson perturbation” (with A. D. Barbour).
European series in Applied
and Industrial Mathematics: Probability and Statistics,
3
(1999),
131150.

“A Probabilistic Proof of Stein's factors”.
Journal of Applied Probability,
36
(1999),
287290.

“Verifying Edges for Visual Inspection Purposes”
(with W. Wen).
Pattern Recognition Letters,
20
(1999),
315328.

“Point processes in time and Stein's method”
(with A. D. Barbour and T. C. Brown).
Stochastics and Stochastics Reports,
65
(1998),
127151.

“On the Variance to Mean Ratio for Random Variables from Markov Chains and
Point Processes”
(with T. C. Brown and K. Hamza).
Journal of Applied Probability,
35
(1998),
303312.

“On the rate of Poisson process approximation to a Bernoulli
processi”.
Journal of Applied Probability,
34
(1997),
898907.

“On Poisson approximation to the partial sum process of a Markov
chain”
(with S. W. He).
Stochastic Processes and their
Applications,
68
(1997),
101111.

“On using the first difference in SteinChen
method”.
Annals of Applied Probability,
7
(1997),
899916.

“On Metrics in Point Process
Approximation”
(with T. C. Brown).
Stochastics and Stochastics Reports,
52
(1995),
247263.

“On SteinChen factors for Poisson
approximation”
(with T. C. Brown).
Statistics and Probability Letters,
23
(1995),
327332.

“Weak Convergence of Markov Processes with Extended
Generators”.
Annals of Probability,
22
(1994),
21832202.

“A Note on the Prohorov Distance between a Counting Process and
a Poisson Process”.
Stochastics and Stochastics Reports,
45
(1993),
6177.

“Weak Convergence of Jump Processes”.
Seminaire de Probabilites XXVI, Lecture Notes in Mathematics, SpringerVerlag
1526
(1992),
3246.
Recent Grants
ARC Discovery Project Grant for 20192021 (P~Vesk,
N~Golding, Y~Wang, A~Xia),
project title: Integrating Niches, Interactions \& Dispersal in Species Distribution Models.
ARC Discovery Project Grant for 20152017 (jointly with A Barbour,
P Pollett, N Ross, M Luczak, G Reinert, A Roellin, E Pekoz),
project title:
Random Discrete Structures: Approximations and Applications.
ARC Discovery Project Grant for 20122014 (jointly with K Borovkov, A Barbour,
P Pollett, A Novikov, M Luczak, G Reinert),
project title: Random Network Models with Applications in Biology.
NHMRC Project Grant for 2012 (jointly with
W Wen, M Wright and Y He),
project title: Genetic and environmental determinants of brain
networks in ageing.
Teaching Responsibilities for 2019
MAST20004 Probability,
MAST90019 Random Processes.
The MelbournePeking forum 25/08/2015  28/08/2015
An introduction of Peking University.
Applied Mathematics at Peking University.
Pure Mathematics at Peking University.
Beijing International Center for Mathematical Research (BICMR).
Statistics at Peking University.
Probability at Peking University.
Discrete Mathematics at Peking University.
Some useful links
ARC Centre of Excellence for Mathematics and Statistics
of Complex Systems;
The International Statistical Institute;
Statistical Job Announcements
in Australia and New Zealand;
The Probability Web;
American Mathematical Society.
This page was updated on
18/06/2019
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