A. Alfonsi, Affine diffusions and Related Processes: Simulation, Theory and Applications (Bocconi Springer Series), vol. 6. Cham, Switzerland: Springer, 2015.
B. Arras and Y. Swan, "A stroll along the gamma," Stochastic Process. Appl., vol. 127, no. 11, pp. 3661-3688, 2017.
S. ArtStein, K. M. Ball, F. Barthe, and A. Naor, "On the rate of convergence in the entropic central limit theorem," Probab. Theory Rel. Fields, vol. 129, no. 3, pp. 381-390, Jul. 2004.
K. Ball, F. Barthe, and A. Naor, "Entropy jumps in the presence of a spectral gap," Duke Math. J., vol. 119, no. 1, pp. 41-63, 2003.
D. Bakry and M. Emery, "Diffusions hypercontractives," Séminaire Probabilités Strasbourg, vol. 19, no. 12, pp. 177-206, 1985.
D. Bakry, I. Gentil, and M. Ledoux, "Analysis and geometry of Markov diffusion operators," in Grundlehren der Mathematischen Wissenschaften, vol. 348. Berlin, Germany: Springer, 2014.
A. R. Barron, "Entropy and the central limit theorem," Ann. Probab., vol. 14, no. 1, pp. 336-342, 1986.
A. R. Barron, "Monotonic central limit theorem for densities," Dept. Statist., Stanford Univ., Stanford, CA, USA, Tech. Rep. 50, 1984.
L. Brown, A. DasGupta, L. R. Haff, and W. E. Strawderman, "The heat equation and Stein's identity: Connections, applications," J. Statist. Planning Inference, vol. 136, no. 7, pp. 2254-2278, 2006.
J. C. Cox, J. E. Ingersoll, Jr., and S. A. Ross, "An intertemporal general equilibrium model of asset prices," Econometrica, vol. 53, no. 2, pp. 363-384, 1985.
J. C. Cox, J. E. Ingersoll, Jr., and S. A. Ross, "A theory of the term structure of interest rates," Econometrica, vol. 53, no. 2, pp. 385-407, 1985.
R. E. Gaunt, A. M. Pickett, and G. Reinert, "Chi-square approximation by Stein's method with application to Pearson's statistic," Ann. Appl. Probab., vol. 27, no. 2, pp. 720-756, 2017.
D. Guo, S. Shamai (Shitz), and S. Verdú, "Mutual information and minimum mean-square error in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, no. 4, pp. 1261-1282, Apr. 2005.
D. Guo, S. Shamai (Shitz), and S. Verdú, "Additive non-Gaussian noise channels: Mutual information and conditional mean estimation," in Proc. Int. Symp. Inf. Theory (ISIT), Sep. 2005, pp. 719-723.
D. Guo, S. Shamai (Shitz), and S. Verdú, "Proof of entropy power inequalities via MMSE," in Proc. Int. Symp. Inf. Theory (ISIT), 2006, pp. 1011-1015.
D. Guo, S. Shamai (Shitz), and S. Verdú, "Mutual information and conditional mean estimation in Poisson channels," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 1837-1849, May 2008.
J. Jiao, K. Venkat, and T. Weissman, "Relations between information and estimation in discrete-time Lévy channels," IEEE Trans. Inf. Theory, vol. 63, no. 6, pp. 3579-3594, Jun. 2017.
O. Johnson, Information Theory and the Central Limit Theorem. London, U.K.: Imperial College Press, 2004.
O. Johnson and A. Barron, "Fisher information inequalities and the central limit theorem," Probab. Theory Rel. Fields, vol. 129, no. 3, pp. 391-409, Jul. 2004.
K. Kawazu and S. Watanabe, "Branching processes with immigration and related limit theorems," Theory Probab. Appl., vol. 16, no. 1, pp. 36-54, 1971.
C. Ley, G. Reinert, and Y. Swan, "Stein's method for comparison of univariate distributions," Probab. Surv., vol. 14, pp. 1-52, Jan. 2017.
C. Ley and Y. Swan, "Stein's density approach and information inequalities," Electron. Commun. Probab., vol. 18, no. 7, pp. 1-14, 2013.
Z.-H. Li, "Branching processes with immigration and related topics," Frontiers Math. China, vol. 1, no. 1, pp. 73-97, 2006.
A. Lozano, A. M. Tulino, and S. Verdú, "Optimum power allocation for parallel Gaussian channels with arbitrary input distributions," IEEE Trans. Inf. Theory, vol. 52, no. 7, pp. 3033-3051, Jul. 2006.
H. M. Luk, "Stein's method for the Gamma distribution and related statistical applications," Ph.D. dissertation, Faculty Graduate School, Appl. Math., Univ. Southern California, Los Angeles, CA, USA, 1994.
O. Mazet, "Classification des semi-groupes de diffusion sur R associés à une famille de polynômes orthogonaux," Séminaire Probabilités, vol. 31, no. 4, pp. 40-53, 1997.
I. Nourdin and G. Peccati, Normal Approximations With Malliavin Calculus: From Stein's Method to Universality (Cambridge Tracts in Mathematics), vol. 192. Cambridge, U.K.: Cambridge Univ. Press, 2012.
I. Nourdin, G. Peccati, and Y. Swan, "Entropy and the fourth moment phenomenon," J. Funct. Anal., vol. 266, pp. 3170-3207, Mar. 2014.
I. Nourdin, G. Peccati, and Y. Swan, "Integration by parts and representation of information functionals," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun./Jul. 2014, pp. 2217-2221.
D. P. Palomar and S. Verdu, "Representation of mutual information via input estimates," IEEE Trans. Inf. Theory, vol. 53, no. 2, pp. 453-470, Feb. 2007.
S. Park, E. Serpedin, and K. Qaraqe, "On the equivalence between Stein and De Bruijn identities," IEEE Trans. Inf. Theory, vol. 58, no. 12, pp. 7045-7067, Dec. 2012.
O. Rioul, "Information theoretic proofs of entropy power inequalities," IEEE Trans. Inf. Theory, vol. 57, no. 1, pp. 33-55, Jan. 2011.
I. Sason, "Improved lower bounds on the total variation distance for the Poisson approximation," Statist. Probab. Lett., vol. 83, no. 10, pp. 2422-2431, 2013.
I. Sason, "Entropy bounds for discrete random variables via maximal coupling," IEEE Trans. Inf. Theory, vol. 59, no. 11, pp. 7118-7131, Nov. 2013.
N. A. Shevchenko, J. E. Prilepsky, S. A. Derevyanko, A. Alvarado, P. Bayvel, and S. K. Turitsyn, "A lower bound on the per soliton capacity of the nonlinear optical fibre channel," in Proc. IEEE Inf. Theory Workshop-Fall (ITW), Oct. 2015, pp. 104-108.
A. J. Stam, "Some inequalities satisfied by the quantities of information of Fisher and Shannon," Inf. Control, vol. 2, no. 2, pp. 101-112, Jun. 1959.
C. Stein, Approximate Computation of Expectations (Lecture Notes-Monograph Series), vol. 7. Hayward, CA, USA: Institute of Mathematical Statistics, 1986.
C. M. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Statist., vol. 9, no. 6, pp. 1135-1151, 1981.
A. M. Tulino and S. Verdú, "Monotonic decrease of the non-Gaussianness of the sum of independent random variables: A simple proof," IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4295-4297, Sep. 2006.
T. M. Cover and J. A. Thomas, Elements of Information Theory. Hoboken, NJ, USA: Wiley, 2012.
Y. Wu and S. Verdú, "MMSE dimension," IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4857-4879, Aug. 2011.