A. A. Borovkov, A. A. Mogul'skii, “Integro-local theorems for sums of independent random vectors in the series scheme”, Mat. Zametki, 79:4 (2006), 505–521; Math. Notes, 79:4 (2006), 468

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Matematicheskie Zametki, 2006, Volume 79, Issue 4, Pages 505–521
DOI: https://doi.org/10.4213/mzm2721 (Mi mzm2721)

This article is cited in 14 scientific papers (total in 14 papers)

Integro-local theorems for sums of independent random vectors in the series scheme

A. A. Borovkov, A. A. Mogul'skii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Full-text PDF (294 kB) Citations (14)

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DOI: https://doi.org/10.4213/mzm2721

Abstract: Let

S (n) = ξ (1) + \dots + ξ (n)

$S(n)=\xi(1)+\dots+\xi(n)$ be a sum of independent random vectors

$\xi(i)=\xi_{(n)}(i)$ with general distribution depending on a parameter

$n$ . We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability

$\mathsf P(S(n)\in\Delta[x))$ , where

$\Delta[x)$ is a cube with edge

$\Delta$ and vertex at a point

$x$ .

Received: 20.05.2004
Revised: 05.09.2005

English version:
Mathematical Notes, 2006, Volume 79, Issue 4, Pages 468–482
DOI: https://doi.org/10.1007/s11006-006-0053-3

Bibliographic databases:

UDC: 519.214

Language: Russian

Citation: A. A. Borovkov, A. A. Mogul'skii, “Integro-local theorems for sums of independent random vectors in the series scheme”, Mat. Zametki, 79:4 (2006), 505–521; Math. Notes, 79:4 (2006), 468–482

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm2721

https://doi.org/10.4213/mzm2721

https://www.mathnet.ru/eng/mzm/v79/i4/p505

This publication is cited in the following 14 articles:

Igor Kortchemski, Cyril Marzouk, “Large deviation local limit theorems and limits of biconditioned planar maps”, Ann. Appl. Probab., 33:5 (2023)
L. V. Rozovskii, “Integro-local CLT for sums of independent nonlattice random vectors”, Theory Probab. Appl., 64:1 (2019), 27–40
L. V. Rozovskii, “On integro-local CLT for sums of independent random vectors”, Theory Probab. Appl., 64:4 (2020), 564–578
A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556
Delbaen F., Kowalski E., Nikeghbali A., “Mod-Phi Convergence”, Int. Math. Res. Notices, 2015, no. 11, 3445–3485
A. A. Borovkov, “Integro-local and local theorems for normal and large deviations of sums of nonidentically distributed random variables in the scheme of series”, Theory Probab. Appl., 54:4 (2010), 571–587
A. A. Mogulskii, “Integralnye i integro-lokalnye teoremy dlya summ sluchainykh velichin s semieksponentsialnymi raspredeleniyami”, Sib. elektron. matem. izv., 6 (2009), 251–271
A. A. Mogulskiǐ, Ch. Pagma, “Superlarge deviations for sums of random variables with arithmetical super-exponential distributions”, Siberian Adv. Math., 18:3 (2008), 185–208
A. A. Mogul'skii, “An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions”, Siberian Math. J., 49:4 (2008), 669–683
A. A. Borovkov, A. A. Mogul'skii, “On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. I”, Theory Probab. Appl., 53:2 (2009), 301–311
A. A. Borovkov, A. A. Mogul'skii, “On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. II”, Theory Probab. Appl., 53:4 (2009), 573–593
A. A. Borovkov, A. A. Mogul'skii, “Integro-local and integral theorems for sums of random variables with semiexponential distributions”, Siberian Math. J., 47:6 (2006), 990–1026
A. A. Mogul'skii, “Large deviations of the first passage time for a random walk with semiexponentially distributed jumps”, Siberian Math. J., 47:6 (2006), 1084–1101
A. A. Borovkov, A. A. Mogul'skii, “On large and superlarge deviations for sums of independent random vectors under the Cramer condition. I”, Theory Probab. Appl., 51:2 (2007), 227–255

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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