central limit theorem,
sum of independent random variables,
normal approximation,
Poisson random sum,
convergence rate estimate,
asymprorically exact constant,
risk process,
smoothing,
Fourier--Stiltjes transform.
Subject:
Convergence rate estimates in the central limit theorem for sums of independent random variables, analytical methods of probability
Main publications:
I. Shevtsova, “On the accuracy of the approximation of the complex exponent by the first terms of its Taylor expansion with applications”, Journal of Mathematical Analysis and Applications, 418 (2014), 185–210
I. G. Shevtsova, “O tochnosti normalnoi approksimatsii dlya obobschennykh puassonovskikh raspredelenii”, TVP, 58:1 (2013), 152–176
Irina Shevtsova, “Moment-type estimates with asymptotically optimal structure for the accuracy of the normal approximation”, Annales Mathematicae et Informaticae, 39 (2012), 241–307
I. G. Shevtsova, “Momentnye otsenki tochnosti normalnoi approksimatsii s utochnennoi strukturoi dlya summ nezavisimykh simmetrichnykh sluchainykh velichin”, TVP, 57:3 (2012), 499–532; Theory Probab. Appl., 57:3 (2013), 468–496
I. G. Shevtsova, “Ob asimptoticheski pravilnykh postoyannykh v neravenstve Berri–Esseena–Katsa”, TVP, 55:2 (2010), 271–304; Theory Probab. Appl., 55:2 (2011), 225–252
V. Korolev, I. Shevtsova, “An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums”, Scandinavian Actuarial Journal, 2012:2 (2012), 81–105
I. G. Shevtsova, “Convergence rate estimates in the global CLT for compound mixed Poisson distributions”, Teor. Veroyatnost. i Primenen., 63:1 (2018), 89–116; Theory Probab. Appl., 63:1 (2018), 72–93
I. G. Shevtsova, “A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums”, Teor. Veroyatnost. i Primenen., 62:2 (2017), 345–364; Theory Probab. Appl., 62:2 (2018), 278–294
I. G. Shevtsova, “On the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements”, Inform. Primen., 7:1 (2013), 124–125
I. G. Shevtsova, “On the accuracy of the normal approximation to compound Poisson distributions”, Teor. Veroyatnost. i Primenen., 58:1 (2013), 152–176; Theory Probab. Appl., 58:1 (2014), 138–158
I. G. Shevtsova, “Moment estimates for the exactness of normal approximation with specified structure for sums of independent symmetrical random variables”, Teor. Veroyatnost. i Primenen., 57:3 (2012), 499–532; Theory Probab. Appl., 57:3 (2013), 468–496
Yu. S. Nefedova, I. G. Shevtsova, “Nonuniform estimates of convergence rate in the central limit theorem”, Teor. Veroyatnost. i Primenen., 57:1 (2012), 62–97; Theory Probab. Appl., 57:1 (2013), 28–59
Yu. S. Nefedova, I. G. Shevtsova, “On the accuracy of the normal approximation to distributions of Poisson random sums”, Inform. Primen., 5:1 (2011), 39–45
V. Yu. Korolev, I. G. Shevtsova, “A new moment estimate of the convergence rate in the Lyapunov theorem”, Teor. Veroyatnost. i Primenen., 55:3 (2010), 577–582; Theory Probab. Appl., 55:3 (2011), 505–509
I. G. Shevtsova, “On the asymptotically exact constants in the Berry–Esseen–Katz inequality”, Teor. Veroyatnost. i Primenen., 55:2 (2010), 271–304; Theory Probab. Appl., 55:2 (2011), 225–252
M. O. Gaponova, I. G. Shevtsova, “Asymptotic estimates of the absolute constant in the Berry–Esseen inequality for distribution with unbounded third moment”, Inform. Primen., 3:4 (2009), 41–56
I. G. Shevtsova, “Some estimates for characteristic functions with an application to sharpening the Mises inequality”, Inform. Primen., 3:3 (2009), 69–78
V. Yu. Korolev, I. G. Shevtsova, “An upper estimate for the absolute constant in the Berry–Esseen inequality”, Teor. Veroyatnost. i Primenen., 54:4 (2009), 671–695; Theory Probab. Appl., 54:4 (2010), 638–658
I. G. Shevtsova, “Some non-uniform estimates of convergence rate in the central limit theorem for sums of independent random variables with bounded densities”, Sistemy i Sredstva Inform., 2006, no. special issue, 286–308
17.
I. G. Shevtsova, “Sharpening of the upper-estimate of the absolute constant in the Berry–Esseen inequality”, Teor. Veroyatnost. i Primenen., 51:3 (2006), 622–626; Theory Probab. Appl., 51:3 (2007), 549–553
V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. II”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 555–564; Theory Probab. Appl., 50:3 (2006), 473–482
V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. I”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 353–366; Theory Probab. Appl., 50:2 (2006), 298–310
I. G. Shevtsova, “Errata to the paper in TVP, v. 55, no. 2, p. 271–304”, Teor. Veroyatnost. i Primenen., 56:1 (2011), 205–206; Theory Probab. Appl., 56:1 (2012), 178–179
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