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References
- Arfken, George. Mathematical methods for physicists. Academic Press, New York-London 1966 xvi+654 pp. MR0205512
- Barbour, A. D. Stein's method and Poisson process convergence. A celebration of applied probability. J. Appl. Probab. 1988, Special Vol. 25A, 175--184. MR0974580
- Barbour, A. D. Stein's method for diffusion approximations. Probab. Theory Related Fields 84 (1990), no. 3, 297--322. MR1035659
- Barndorff-Nielsen, O.; Halgreen, Christian. Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 38 (1977), no. 4, 309--311. MR0436260
- Barndorff-Nielsen, O.; Kent, J.; Sorensen, M. Normal variance-mean mixtures and $z$ distributions. Internat. Statist. Rev. 50 (1982), no. 2, 145--159. MR0678296
- Berry, Andrew C. The accuracy of the Gaussian approximation to the sum of independent variates. Trans. Amer. Math. Soc. 49, (1941). 122--136. MR0003498
- BIBBY, B. M., and SORENSEN, M. Hyperbolic Processes in Finance. In S. Rachev (ed.), Handbook of Heavy Tailed Distributions in Finance (2003), pp. 211--248. Amsterdam: Elsevier Science.
- BLAISDELL, B. A measure of the similarity of sets of sequences not requiring sequence alignment. Proc. Natl. Acad. Sci. USA 83 (1986), pp. 5155--5159.
- Chatterjee, Sourav; Fulman, Jason; Rollin, Adrian. Exponential approximation by Stein's method and spectral graph theory. ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), 197--223. MR2802856
- Chen, Louis H. Y. Poisson approximation for dependent trials. Ann. Probability 3 (1975), no. 3, 534--545. MR0428387
- Chen, Louis H. Y.; Goldstein, Larry; Shao, Qi-Man. Normal approximation by Stein's method. Probability and its Applications (New York). Springer, Heidelberg, 2011. xii+405 pp. ISBN: 978-3-642-15006-7 MR2732624
- COLLINS, P. J. Differential and Integral Equations. Oxford University Press, 2006.
- DÖBLER, C. Distributional transformations without orthogonality relations. arXiv:1312.6093, 2013.
- Durrett, Richard. Stochastic calculus. A practical introduction. Probability and Stochastics Series. CRC Press, Boca Raton, FL, 1996. x+341 pp. ISBN: 0-8493-8071-5 MR1398879
- Eberlein, Ernst; v. Hammerstein, Ernst August. Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes. Seminar on Stochastic Analysis, Random Fields and Applications IV, 221--264, Progr. Probab., 58, Birkhauser, Basel, 2004. MR2096291
- Esseen, Carl-Gustav. Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77, (1945). 1--125. MR0014626
- Finlay, Richard; Seneta, Eugene. Option pricing with VG-like models. Int. J. Theor. Appl. Finance 11 (2008), no. 8, 943--955. MR2492088
- GAUNT, R. E. phRates of Convergence of Variance-Gamma Approximations via Stein's Method. DPhil thesis, University of Oxford, 2013.
- GAUNT, R. E. Uniform bounds for expressions involving modified Bessel functions. Preprint 2013.
- GAUNT, R. E. On Stein's Method for products of normal, gamma and beta random variables and a generalisation of the zero bias coupling. Preprint 2014.
- Goldstein, Larry; Reinert, Gesine. Stein's method and the zero bias transformation with application to simple random sampling. Ann. Appl. Probab. 7 (1997), no. 4, 935--952. MR1484792
- Goldstein, Larry; Rinott, Yosef. Multivariate normal approximations by Stein's method and size bias couplings. J. Appl. Probab. 33 (1996), no. 1, 1--17. MR1371949
- HOLM, H. and ALOUINI, M--S. Sum and Difference of two squared correlated Nakagami variates with the McKay distribution. phIEEE Transactions on Communications. 52 (2004), pp 1367-1376.
- LEY, C. and SWAN, Y. A unified approach to Stein characterizations. arXiv:1105.4925, 2011.
- Linetsky, Vadim. The spectral representation of Bessel processes with constant drift: applications in queueing and finance. J. Appl. Probab. 41 (2004), no. 2, 327--344. MR2052575
- Lippert, Ross A.; Huang, Haiyan; Waterman, Michael S. Distributional regimes for the number of $k$-word matches between two random sequences. Proc. Natl. Acad. Sci. USA 99 (2002), no. 22, 13980--13989 (electronic). MR1944413
- Luk, Ho Ming. Stein's method for the Gamma distribution and related statistical applications. Thesis (Ph.D.)–University of Southern California. ProQuest LLC, Ann Arbor, MI, 1994. 74 pp. MR2693204
- MADAN, D. B. and SENETA, E. The Variance Gamma (V.G.) Model for Share Market Returns. Journal of Business 63 (1990), pp. 511--524.
- Nourdin, Ivan; Peccati, Giovanni. Stein's method on Wiener chaos. Probab. Theory Related Fields 145 (2009), no. 1-2, 75--118. MR2520122
- NIST handbook of mathematical functions. Edited by Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert and Charles W. Clark. With 1 CD-ROM (Windows, Macintosh and UNIX). U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press, Cambridge, 2010. xvi+951 pp. ISBN: 978-0-521-14063-8 MR2723248
- Pekez, Erol A.; Rollin, Adrian. New rates for exponential approximation and the theorems of Rényi and Yaglom. Ann. Probab. 39 (2011), no. 2, 587--608. MR2789507
- Pekez, Erol A.; Rollin, Adrian; Ross, Nathan. Degree asymptotics with rates for preferential attachment random graphs. Ann. Appl. Probab. 23 (2013), no. 3, 1188--1218. MR3076682
- PICKETT, A. phRates of Convergence of χ^2 Approximations via Stein's Method. DPhil thesis, University of Oxford, 2004.
- PIKE, J. and REN, H. Stein's method and the Laplace distribution. arXiv:1210.5775, 2012.
- RAIC, M. Normal approximation by Stein's method. In: Proceedings of the 7th Young Statisticians Meeting (2003), pp. 71--97.
- Reinert, Gesine. Three general approaches to Stein's method. An introduction to Stein's method, 183--221, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 4, Singapore Univ. Press, Singapore, 2005. MR2235451
- Lothaire, M. Applied combinatorics on words. A collective work by Jean Berstel, Dominique Perrin, Maxime Crochemore, Eric Laporte, Mehryar Mohri, Nadia Pisanti, Marie-France Sagot, Gesine Reinert, Sophie Schbath, Michael Waterman, Philippe Jacquet, Wojciech Szpankowski, Dominique Poulalhon, Gilles Schaeffer, Roman Kolpakov, Gregory Koucherov, Jean-Paul Allouche and Valérie Berthé. With a preface by Berstel and Perrin. Encyclopedia of Mathematics and its Applications, 105. Cambridge University Press, Cambridge, 2005. xvi+610 pp. ISBN: 978-0-521-84802-2; 0-521-84802-4 MR2165687
- Reinert, Gesine; Rollin, Adrian. Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition. Ann. Probab. 37 (2009), no. 6, 2150--2173. MR2573554
- Reinert, Gesine; Chew, David; Sun, Fengzhu; Waterman, Michael S. Alignment-free sequence comparison. I. Statistics and power. J. Comput. Biol. 16 (2009), no. 12, 1615--1634. MR2578699
- Scott, David J.; Wurtz, Diethelm; Dong, Christine; Tran, Thanh Tam. Moments of the generalized hyperbolic distribution. Comput. Statist. 26 (2011), no. 3, 459--476. MR2833142
- Stein, Charles. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, pp. 583--602. Univ. California Press, Berkeley, Calif., 1972. MR0402873
- Stein, Charles. Approximate computation of expectations. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 7. Institute of Mathematical Statistics, Hayward, CA, 1986. iv+164 pp. ISBN: 0-940600-08-0 MR0882007
- Stein, Charles; Diaconis, Persi; Holmes, Susan; Reinert, Gesine. Use of exchangeable pairs in the analysis of simulations. Stein's method: expository lectures and applications, 1--26, IMS Lecture Notes Monogr. Ser., 46, Inst. Math. Statist., Beachwood, OH, 2004. MR2118600
- WINKELBAUER, A. Moments and absolute moments of the normal distribution, arXiv:1209.4340, 2012.
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