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Journal articles on the topic 'Theorems of large deviations'

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Published: 4 June 2021

Last updated: 11 February 2022

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1

Kifer, Yuri, and S. R. S. Varadhan. "Nonconventional large deviations theorems." Probability Theory and Related Fields 158, no. 1-2 (2013): 197–224. http://dx.doi.org/10.1007/s00440-013-0481-4.

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2

Goldie, C. M. "Limit Theorems for Large Deviations." Bulletin of the London Mathematical Society 25, no. 4 (1993): 409–10. http://dx.doi.org/10.1112/blms/25.4.409.

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3

Bingham, N. H. "Tauberian theorems and large deviations." Stochastics 80, no. 2-3 (2008): 143–49. http://dx.doi.org/10.1080/17442500701830365.

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4

Batkovich, D. V. "Local limit theorems for large deviations." Journal of Mathematical Sciences 188, no. 6 (2013): 641–54. http://dx.doi.org/10.1007/s10958-013-1154-7.

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5

Liptser, Robert sh, and Anatolii a. pukhalskii. "Limit theorems on large deviations for semimartingales." Stochastics and Stochastic Reports 38, no. 4 (1992): 201–49. http://dx.doi.org/10.1080/17442509208833757.

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6

Kleptsyn, Victor, Dmitry Ryzhov, and Stanislav Minkov. "Special ergodic theorems and dynamical large deviations." Nonlinearity 25, no. 11 (2012): 3189–96. http://dx.doi.org/10.1088/0951-7715/25/11/3189.

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7

Comman, Henri. "Stone-Weierstrass type theorems for large deviations." Electronic Communications in Probability 13 (2008): 225–40. http://dx.doi.org/10.1214/ecp.v13-1370.

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8

Chu, Ba, John Knight, and Stephen Satchell. "Large deviations theorems for optimal investment problems with large portfolios." European Journal of Operational Research 211, no. 3 (2011): 533–55. http://dx.doi.org/10.1016/j.ejor.2010.12.007.

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9

Cattiaux, Patrick, and Fabrice Gamboa. "Large Deviations and Variational Theorems for Marginal Problems." Bernoulli 5, no. 1 (1999): 81. http://dx.doi.org/10.2307/3318614.

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10

Rudzkis, Rimantas, and Aleksej Bakshaev. "General theorems on large deviations for random vectors." Lithuanian Mathematical Journal 57, no. 3 (2017): 367–90. http://dx.doi.org/10.1007/s10986-017-9367-y.

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11

Louani, Djamal. "Large Deviations Limit Theorems for the Kernel Density Estimator." Scandinavian Journal of Statistics 25, no. 1 (1998): 243–53. http://dx.doi.org/10.1111/1467-9469.00101.

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12

Ioffe, Dimitry. "On Some Applicable Versions of Abstract Large Deviations Theorems." Annals of Probability 19, no. 4 (1991): 1629–39. http://dx.doi.org/10.1214/aop/1176990226.

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13

Freidlin, Mark. "Limit Theorems for Large Deviations and Reaction-Diffusion Equations." Annals of Probability 13, no. 3 (1985): 639–75. http://dx.doi.org/10.1214/aop/1176992901.

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14

Malinovskii, V. K. "Limit Theorems for Stopped Random Sequences II: Large Deviations." Theory of Probability & Its Applications 41, no. 1 (1997): 70–90. http://dx.doi.org/10.1137/tprbau000041000001000070000001.

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15

Hwang, Hsien-Kuei. "Large deviations for combinatorial distributions. I. Central limit theorems." Annals of Applied Probability 6, no. 1 (1996): 297–319. http://dx.doi.org/10.1214/aoap/1034968075.

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16

Hwang, Hsien-Kuei. "Large deviations of combinatorial distributions. II. Local limit theorems." Annals of Applied Probability 8, no. 1 (1998): 163–81. http://dx.doi.org/10.1214/aoap/1027961038.

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17

Louani, Djamal. "Some Large Deviations Limit Theorems in Conditional Nonparametric Statistics." Statistics 33, no. 2 (1999): 171–96. http://dx.doi.org/10.1080/02331889908802690.

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18

Bentkus, Vidmantas. "Theorems of large deviations in the multivariate invariance principle." Journal of Multivariate Analysis 41, no. 2 (1992): 297–313. http://dx.doi.org/10.1016/0047-259x(92)90071-m.

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19

Cherfi, Mohamed. "Large deviations theorems in nonparametric regression on functional data." Comptes Rendus Mathematique 349, no. 9-10 (2011): 583–85. http://dx.doi.org/10.1016/j.crma.2011.04.011.

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20

Avilés López, Antonio, and José Miguel Zapata García. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations." Mathematics 8, no. 10 (2020): 1848. http://dx.doi.org/10.3390/math8101848.

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We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By mea

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21

ATAPOUR, MAHSHID, and NEAL MADRAS. "Large Deviations and Ratio Limit Theorems for Pattern-Avoiding Permutations." Combinatorics, Probability and Computing 23, no. 2 (2013): 161–200. http://dx.doi.org/10.1017/s0963548313000576.

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For a fixed permutation τ, let$\mathcal{S}_N(\tau)$be the set of permutations onNelements that avoid the pattern τ. Madras and Liu (2010) conjectured that$\lim_{N\rightarrow\infty}\frac{|\mathcal{S}_{N+1}(\tau)|}{ |\mathcal{S}_N(\tau)|}$exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the 720 permutations of length 6). We also consider permutations drawn at random from$\mathcal{S}_N(\tau)$, and we investigate properties of their graphs (viewing permutations as functi

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22

Chi, Zhiyi. "Strong renewal theorems with infinite mean beyond local large deviations." Annals of Applied Probability 25, no. 3 (2015): 1513–39. http://dx.doi.org/10.1214/14-aap1029.

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23

Timashev, A. N. "Integral Limit Theorems on Large Deviations for Multidimensional Hypergeometric Distribution." Theory of Probability & Its Applications 47, no. 1 (2003): 91–98. http://dx.doi.org/10.1137/s0040585x97979457.

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24

Zaigraev, A. Yu. "Limit theorems for conditional distributions with regard for large deviations." Ukrainian Mathematical Journal 51, no. 8 (1999): 1188–200. http://dx.doi.org/10.1007/bf02592507.

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25

Račkauskas, A. "Limit theorems for large deviations probabilities of certain quadratic forms." Lithuanian Mathematical Journal 37, no. 4 (1997): 402–15. http://dx.doi.org/10.1007/bf02465581.

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26

Kasparavičiūtė, Aurelija, and Leonas Saulis. "Large deviations for weighted random sums." Nonlinear Analysis: Modelling and Control 18, no. 2 (2013): 129–42. http://dx.doi.org/10.15388/na.18.2.14017.

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In the present paper we consider weighted random sums ZN = ∑j=1NajXj, where 0 ≤ aj < ∞, N denotes a non-negative integer-valued random variable, and {X, Xj , j = 1, 2,...} is a family of independent identically distributed random variables with mean EX = µ and variance DX = σ2 > 0. Throughout this paper N is independent of {X, Xj , j = 1, 2,...} and, for definiteness, it is assumed Z0 = 0. The main idea of the paper is to present results on theorems of large deviations both in the Cramér and power Linnik zones for a sum ~ZN = (ZN − EZN )(DZN )−1/2 , exponential inequalities for a tail pr

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27

Bakay, Gavriil A., and Aleksandr V. Shklyaev. "Large deviations of generalized renewal process." Discrete Mathematics and Applications 30, no. 4 (2020): 215–41. http://dx.doi.org/10.1515/dma-2020-0020.

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AbstractLet (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i < ∞, be independent identically distributed random vectors, η(i) be nonnegative random variables, the vector (ξ(1), η(1)) satisfy the Cramer condition. On the base of renewal process, NT = max{k : η(1) + … + η(k) ≤ T} we define the generalized renewal process ZT = $\begin{array}{} \sum_{i=1}^{N_T} \end{array}$ξ(i). Put IΔT(x) = {y ∈ ℝd : xj ≤ yj < xj + ΔT, j = 1, …, d}. We find asymptotic formulas for the probabilities P(ZT ∈ IΔT(x)) as ΔT → 0 and P(ZT = x) in non-lattice and arithmetic cases, respectively, in a wide range of x values, including nor

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28

REY-BELLET, LUC, and LAI-SANG YOUNG. "Large deviations in non-uniformly hyperbolic dynamical systems." Ergodic Theory and Dynamical Systems 28, no. 2 (2008): 587–612. http://dx.doi.org/10.1017/s0143385707000478.

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AbstractWe prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hénon-type attractors.

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29

Sang, Hailin, and Yimin Xiao. "Exact moderate and large deviations for linear random fields." Journal of Applied Probability 55, no. 2 (2018): 431–49. http://dx.doi.org/10.1017/jpr.2018.28.

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Abstract By extending the methods of Peligrad et al. (2014), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.

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30

Shwartz, Adam, and Alan Weiss. "Induced rare events: analysis via large deviations and time reversal." Advances in Applied Probability 25, no. 03 (1993): 667–89. http://dx.doi.org/10.1017/s000186780002560x.

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When a subsystem goes into an infrequent state, how does the remainder of the system behave? We show how to calculate the relevant distributions using the notions of reversed time for Markov processes and large deviations. For ease of exposition, most of the work deals with a specific queueing model due to Flatto, Hahn, and Wright. However, we show how the theorems may be applied to much more general jump-Markov systems. We also show how the tools of time-reversal and large deviations complement each other to yield general theorems. We show that the way a constant coefficient process approache

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31

Shwartz, Adam, and Alan Weiss. "Induced rare events: analysis via large deviations and time reversal." Advances in Applied Probability 25, no. 3 (1993): 667–89. http://dx.doi.org/10.2307/1427529.

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Abstract:

When a subsystem goes into an infrequent state, how does the remainder of the system behave? We show how to calculate the relevant distributions using the notions of reversed time for Markov processes and large deviations. For ease of exposition, most of the work deals with a specific queueing model due to Flatto, Hahn, and Wright. However, we show how the theorems may be applied to much more general jump-Markov systems.We also show how the tools of time-reversal and large deviations complement each other to yield general theorems. We show that the way a constant coefficient process approaches

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32

Mirakhmedov, Sherzod Mira'zam. "The probability of large deviations for the sum functions of spacings." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–22. http://dx.doi.org/10.1155/ijmms/2006/58738.

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Let0=U0,n≤U1,n≤⋯≤Un−1,n≤Un,n=1be an ordered sample from uniform[0,1]distribution, andDin=Ui,n−Ui−1,n,i=1,2,…,n;n=1,2,…,be their spacings, and letf1n,…,fnnbe a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statisticsRn(D)=f1n(nD1n)+⋯+fnn(nDnn)are proved. Application of these theorems for determination of the intermediate efficiencies of the tests based onRn(D)-type statistic is presented here too.

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33

Chaganty, Narasinga R., and Jayaram Sethuraman. "Multidimensional strong large deviation theorems." Journal of Statistical Planning and Inference 55, no. 3 (1996): 265–80. http://dx.doi.org/10.1016/s0378-3758(96)00083-3.

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34

Rozovskii, L. V. "On the Accuracy of Approximation in Limit Theorems for Large Deviations." Theory of Probability & Its Applications 31, no. 2 (1987): 255–68. http://dx.doi.org/10.1137/1131032.

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35

Mikami, Toshio. "Large Deviations Theorems for Empirical Measures in Freidlin-Wentzell Exit Problems." Annals of Probability 19, no. 1 (1991): 58–82. http://dx.doi.org/10.1214/aop/1176990536.

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36

Borovkov, A. A., and A. A. Mogulskii. "Integro-Local Limit Theorems Including Large Deviations for Sumsof Random Vectors." Theory of Probability & Its Applications 43, no. 1 (1999): 1–12. http://dx.doi.org/10.1137/s0040585x97976623.

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37

Nagel, Jan. "Nonstandard limit theorems and large deviations for the Jacobi beta ensemble." Random Matrices: Theory and Applications 03, no. 03 (2014): 1450012. http://dx.doi.org/10.1142/s2010326314500129.

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In this paper, we show weak convergence of the empirical eigenvalue distribution and of the weighted spectral measure of the Jacobi ensemble, when one or both parameters grow faster than the dimension n. In these cases, the limit measure is given by the Marchenko–Pastur law and the semicircle law, respectively. For the weighted spectral measure, we also prove large deviation principles under this scaling, where the rate functions are those of the other classical ensembles.

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38

Nagaev, Alexander V., and Alexander Yu Zaigraev. "Multidimensional Limit Theorems Allowing Large Deviations for Densities of Regular Variation." Journal of Multivariate Analysis 67, no. 2 (1998): 385–97. http://dx.doi.org/10.1006/jmva.1998.1773.

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39

Nagaev, S. V., and V. I. Vakhtel. "Limit theorems for probabilities of large deviations of a Galton–Watson process." Discrete Mathematics and Applications 13, no. 1 (2003): 1–26. http://dx.doi.org/10.1515/156939203321669537.

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40

Mikami, Toshio. "Large deviations and central limit theorems for Eyraud-Farlie-Gumbel-Morgenstern processes." Statistics & Probability Letters 35, no. 1 (1997): 73–78. http://dx.doi.org/10.1016/s0167-7152(96)00218-0.

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41

Faggionato, Alessandra, and Vittoria Silvestri. "Random walks on quasi one dimensional lattices: Large deviations and fluctuation theorems." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53, no. 1 (2017): 46–78. http://dx.doi.org/10.1214/15-aihp708.

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42

Kasparavičiūtė, Aurelija, and Leonas Saulis. "Theorems on Large Deviations for Randomly Indexed Sum of Weighted Random Variables." Acta Applicandae Mathematicae 116, no. 3 (2011): 255–67. http://dx.doi.org/10.1007/s10440-011-9641-7.

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43

Chaganty, Narasinga R., and J. Sethuraman. "Multidimensional large deviation local limit theorems." Journal of Multivariate Analysis 20, no. 2 (1986): 190–204. http://dx.doi.org/10.1016/0047-259x(86)90077-1.

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44

Gu, Rongbao. "The large deviations theorem and ergodicity☆." Chaos, Solitons & Fractals 34, no. 5 (2007): 1387–92. http://dx.doi.org/10.1016/j.chaos.2007.01.081.

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45

Niu, Yingxuan. "The large deviations theorem and sensitivity." Chaos, Solitons & Fractals 42, no. 1 (2009): 609–14. http://dx.doi.org/10.1016/j.chaos.2009.01.036.

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46

Smorodina, N. V., and M. M. Faddeev. "Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations." Journal of Mathematical Sciences 167, no. 4 (2010): 550–65. http://dx.doi.org/10.1007/s10958-010-9943-8.

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47

Fang, Lulu, and Min Wu. "A Note on Rényi's ‘Record’ Problem and Engel's Series." Proceedings of the Edinburgh Mathematical Society 61, no. 2 (2018): 363–69. http://dx.doi.org/10.1017/s0013091517000116.

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AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] introduced two interesting discrete Markov processes, namely C-processes and A-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there

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48

Michel, Julien, and Didier Piau. "Large deviations, central limit theorems and Lpconvergence for Young measures and stochastic homogenizations." ESAIM: Probability and Statistics 2 (1998): 135–61. http://dx.doi.org/10.1051/ps:1998105.

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49

Kachurovskii, A. G., and I. V. Podvigin. "Correlations, large deviations, and rates of convergence in ergodic theorems for characteristic functions." Doklady Mathematics 91, no. 2 (2015): 204–7. http://dx.doi.org/10.1134/s1064562415020283.

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50

Chaganty, Narasinga Rao, and Jayaram Sethuraman. "Limit Theorems in the Area of Large Deviations for Some Dependent Random Variables." Annals of Probability 15, no. 2 (1987): 628–45. http://dx.doi.org/10.1214/aop/1176992162.

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