On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables

[1]  Dmitry Zaporozhets,et al.  Absorption probabilities for Gaussian polytopes and regular spherical simplices , 2017, Advances in Applied Probability.

[2]  L. Rozovsky Small deviation probabilities for sums of independent positive random variables , 2007, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy.

[3]  N. Rastegaev On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics , 2018, St. Petersburg Mathematical Journal.

[4]  L. Rozovsky Small Deviation Probabilities of a Sum of Independent Positive Random Variables, the Common Distribution of Which Decreases at Zero Not Faster Than Exponential Function , 2018 .

[5]  Z. Kabluchko,et al.  Expected volumes of Gaussian polytopes, external angles, and multiple order statistics , 2017, Transactions of the American Mathematical Society.

[6]  Small ball probabilities for certain gaussian fields , 2017, 1705.05001.

[7]  A. Nazarov,et al.  The Small Ball Asymptotics in Hilbert Norm for the Kac--Kiefer--Wolfowitz Processes , 2016 .

[8]  Small deviations of sums of correlated stationary Gaussian sequences , 2016, 1606.01072.

[9]  A. A. Khartov A simplified criterion for quasi-polynomial tractability of approximation of random elements and its applications , 2016, J. Complex..

[10]  Saralees Nadarajah,et al.  Acknowledgement of priority: On the result of doney , 2016 .

[11]  L. Rozovsky Probabilities of Small Deviations of the Weighted Sum of Independent Random Variables with Common Distribution That Decreases at Zero Not Faster Than a Power , 2016 .

[12]  L. Rozovsky Small Deviations of Probabilities for Weighted Sum of Independent Positive Random Variables with a Common Distribution That Decreases at Zero Not Faster than a Power , 2016 .

[13]  R. Dudley V.N. Sudakov’s Work on Expected Suprema of Gaussian Processes , 2016 .

[14]  Seok Young Hong,et al.  Small Deviations in $L_2$-norm for Gaussian Dependent Sequences , 2015, 1511.05370.

[15]  N. Rastegaev On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Self-Similar Weight of Generalized Cantor Type , 2015 .

[16]  Alexey A. Khartov,et al.  Asymptotic analysis of average case approximation complexity of Hilbert space valued random elements , 2014, J. Complex..

[17]  L. Rozovsky Small Deviation Probabilities for Sums of Independent Positive Random Variables with a Distribution that Slowly Varies at Zero , 2015 .

[18]  Approximation in Probability of Tensor Product-Type Random Fields of Increasing Parametric Dimension , 2015 .

[19]  A. Kirichenko,et al.  Precise small deviations in L2 of some Gaussian processes appearing in the regression context , 2014 .

[20]  R. S. Pusev,et al.  Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted ₂-norms , 2014 .

[21]  Z. Kabluchko,et al.  Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls , 2014, 1404.6113.

[22]  L. Rozovsky Small Deviations of Series of Independent Nonnegative Random Variables with Smooth Weights , 2014 .

[23]  A. Khartov Approximation complexity of tensor product-type random fields with heavy spectrum , 2013 .

[24]  A. A. Khartov Average approximation of tensor product-type random fields of incresing dimension , 2013 .

[25]  Small deviation probabilities for sums of independent positive random variables whose density has a power decay at zero , 2013 .

[26]  A. Frolov Limit theorems for small deviation probabilities of some iterated Stochastic processes , 2013 .

[27]  A. Frolov Small deviations of iterated processes in the space of trajectories , 2012, 1208.6148.

[28]  M. Gordin CLT for Stationary Normal Markov Chains via Generalized Coboundaries , 2013 .

[29]  A. Nazarov,et al.  Degenerate self‐similar measures, spectral asymptotics and small deviations of Gaussian processes , 2012 .

[30]  M. Lifshits Lectures on Gaussian Processes , 2012 .

[31]  Henryk Wozniakowski,et al.  Average case tractability of non-homogeneous tensor product problems , 2011, J. Complex..

[32]  M. A. Lifshits,et al.  TRACTABILITY OF MULTI-PARAMETRIC EULER AND WIENER INTEGRATED PROCESSES , 2011, 1112.4248.

[33]  M. Denker,et al.  Limit theorems for von Mises statistics of a measure preserving transformation , 2011, 1109.0635.

[34]  L. Rozovsky On small deviations of series of weighted positive random variables , 2011 .

[35]  R. S. Pusev,et al.  Exact small deviation asymptotics for some Brownian functionals , 2011 .

[36]  R. S. Pusev Small Deviations Asymptotics for Matérn Processes and Fields under Weighted Quadratic Norm , 2011 .

[37]  R. S. Pusev Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm , 2010 .

[38]  A. Nazarov,et al.  Small ball probabilities for smooth Gaussian fields and tensor products of compact operators , 2010, 1009.4412.

[39]  A.I.Nazarov,et al.  Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes , 2010, 1009.1252.

[40]  N. Serdyukova Dependence on the Dimension for Complexity of Approximation of Random Fields (in Russian) , 2007, math/0701058.

[41]  R. S. Pusev,et al.  Exact small ball asymptotics in weighted L2-norm for some Gaussian processes , 2009 .

[42]  A. Nazarov Exact L2-Small Ball Asymptotics of Gaussian Processes and the Spectrum of Boundary-Value Problems , 2009 .

[43]  W. Linde,et al.  Small deviations of stable processes and entropy of the associated random operators , 2008, 0804.1883.

[44]  E. Novak,et al.  Tractability of Multivariate Problems , 2008 .

[45]  Aggregation in a one-dimensional stochastic gas model with finite polynomial moments of particle speeds , 2008 .

[46]  F. Aurzada,et al.  On the Small Deviation Problem for Some Iterated Processes , 2008, 0806.2559.

[47]  On Probabilities of Small Deviations for Compound Renewal Processes , 2008 .

[48]  A. Nazarov On a set of transformations of Gaussian random functions , 2008, 0805.1967.

[49]  A. Nazarov Log-level comparison principle for small ball probabilities , 2008, 0805.1773.

[50]  M. Lifshits,et al.  Small deviations of smooth stationary Gaussian processes , 2008, 0803.4238.

[51]  Alexander I. Nazarov,et al.  Small ball probabilities for Gaussian random fields and tensor products of compact operators , 2008 .

[52]  V. Vysotsky Clustering in a stochastic model of one-dimensional gas. , 2007, 0704.0086.

[53]  Wenbo V. Li,et al.  Logarithmic Level Comparison for Small Deviation Probabilities , 2007 .

[54]  Functional large deviations for burgers particle systems , 2007 .

[55]  Wenbo V. Li,et al.  Logarithmic Level Comparison for Small Deviation Probabilities , 2007 .

[56]  Richard C. Bradley,et al.  Introduction to strong mixing conditions , 2007 .

[57]  Elena Shmileva Small ball probabilities for jump Lévy processes from the Wiener domain of attraction , 2006 .

[58]  E. Orsingher,et al.  Exact small deviation asymptotics for the Slepian and Watson processes in the Hilbert norm , 2006 .

[59]  V. Vysotsky On Energy and Clusters in Stochastic Systems of Sticky Gravitating Particles , 2006 .

[60]  W. Linde,et al.  Small Deviations of Gaussian Random Fields in $L_q$-Spaces , 2006, math/0605417.

[61]  Y. Nikitin,et al.  Sharp Small Deviation Asymptotics in the L2-Norm for a Class of Gaussian Processes , 2006 .

[62]  Aggregation in a One-Dimensional Gas Model with Stable Initial Data , 2006 .

[63]  A. Nazarov Logarithmic L2-Small Ball Asymptotics with Respect to a Self-Similar Measure for Some Gaussian Processes , 2006 .

[64]  M. Lifshits,et al.  Small Deviations of Riemann‐Liouville Processes In lq Spaces With Respect To Fractal Measures , 2006 .

[65]  M. Lifshits,et al.  Curse of dimensionality in approximation of random fields , 2006 .

[66]  E. Shmileva Small Ball Probabilities for a Centered Poisson Process of High Intensity , 2005 .

[67]  L. Beghin,et al.  Exact Small Ball Constants for Some Gaussian Processes under the L2-Norm , 2005 .

[68]  M. Lifshits,et al.  Probabilities of randomly centered small balls and quantization in banach spaces , 2004, math/0402220.

[69]  Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation , 2003, cond-mat/0311025.

[70]  A. Nazarov,et al.  Logarithmic L2-small ball asymptotics for some fractional Gaussian processes , 2005 .

[71]  Small deviations of weighted fractional processes and average non–linear approximation , 2004 .

[72]  A. I. Nazarov,et al.  Exact L2-small ball behavior of integrated Gaussian processes and spectral asymptotics of boundary value problems , 2004 .

[73]  H. Holzmann,et al.  THE CENTRAL LIMIT THEOREM FOR STATIONARY MARKOV CHAINS UNDER INVARIANT SPLITTINGS , 2004 .

[74]  Small Ball Probabilities for a Shifted Poisson Process , 2003 .

[75]  J. A. Fill,et al.  Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets , 2003, math/0309391.

[76]  A. Nazarov On the Sharp Constant in the Small Ball Asymptotics of Some Gaussian Processes under L2-Norm , 2003 .

[77]  M. Lifshits,et al.  Small deviations for fractional stable processes , 2003, math/0305092.

[78]  M. Lifshits,et al.  Some exact rates in the functional law of the iterated logarithm , 2002 .

[79]  W. Linde,et al.  Approximation and entropy numbers of Volterra operators with application to Brownian motion , 2002 .

[80]  Jérôme Dedecker,et al.  On the functional central limit theorem for stationary processes , 2000 .

[81]  M. Lifshits,et al.  Chung's Law and The Csáki Function , 1999 .

[82]  Rates of clustering in the Strassen law for random polygons , 1999 .

[83]  Mikhail Lifshits,et al.  On the lower tail probabilities of some random series , 1997 .

[84]  M. Lifshits Gaussian Random Functions , 1995 .

[85]  Mikhail Lifshits,et al.  Necessary and Sufficient Conditions for the Strassen Law of the Iterated Logarithm in Nonuniform Topologies , 1994 .

[86]  B. S. Tsirel'son Stationary Gaussian processes with a finite correlation function , 1994 .

[87]  M. Lifshits,et al.  Strassen-type functional laws for strong topologies , 1993 .

[88]  Exact rate of convergence in Strassen's law of the interated logarithm , 1992 .

[89]  On the Rate of Convergence in the Central Limit Theorem for Weakly Dependent Random Variables , 1992 .

[90]  On the Rate of Clustering in Strassen’s Lil for Brownian Motion , 1992 .

[91]  V. Gorodetskii On the Convergence Rate in the Invariance Principle for Strongly Mixing Sequences , 1984 .

[92]  V. Gorodetskii The Invariance Principle for Stationary Random Fields with a Strong Mixing Condition , 1983 .

[93]  B. Tsirelson A Geometrical Approach to Maximum Likelihood Estimation for Infinite-Dimensional Gaussian Location. I , 1983 .

[94]  I. A. Ibragimov,et al.  Hitting probability of a Gaussian vector with values in a Hilbert space in a sphere of small radius , 1982 .

[95]  Alexander Tikhomirov,et al.  On the Convergence Rate in the Central Limit Theorem for Weakly Dependent Random Variables , 1981 .

[96]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[97]  V. Sudakov,et al.  Geometric Problems in the Theory of Infinite-dimensional Probability Distributions , 1979 .

[98]  On the Central Limit Theorem for Markov Chains , 1979 .

[99]  V. Sudakov,et al.  Extremal properties of half-spaces for spherically invariant measures , 1978 .

[100]  I. Ibragimov A Note on the Central Limit Theorems for Dependent Random Variables , 1975 .

[101]  C. C. Heyde,et al.  On the central limit theorem for stationary processes , 1974 .

[102]  Y. Davydov Mixing Conditions for Markov Chains , 1974 .

[103]  C. Stein A bound for the error in the normal approximation to the distribution of a sum of dependent random variables , 1972 .

[104]  I. Ibragimov,et al.  Independent and stationary sequences of random variables , 1971 .

[105]  Yu. A. Davydov,et al.  The Invariance Principle for Stationary Processes , 1970 .

[106]  Y. Davydov Convergence of Distributions Generated by Stationary Stochastic Processes , 1968 .

[107]  M. Kh. Reznik The Law of the Iterated Logarithm for Some Classes of Stationary Processes , 1968 .

[108]  I. Ibragimov The Central Limit Theorem for Sums of Functions of Independent Variables and Sums of the Form $\sum {f(2^k t)} $ , 1967 .

[109]  V. Strassen An invariance principle for the law of the iterated logarithm , 1964 .

[110]  I. Ibragimov,et al.  A Central Limit Theorem for a Class of Dependent Random Variables , 1963 .

[111]  I. Ibragimov,et al.  Some Limit Theorems for Stationary Processes , 1962 .

[112]  R. Dobrushin Central Limit Theorem for Nonstationary Markov Chains. II , 1956 .