A Bibliographical Guide to Self-Similar Processes and Long-Range Dependence

Self-similar processes are of interest in probability, statistics, physics, turbulence and in modelling random phenomena with long-range dependence. Since the applications are diverse, references are scattered in the literature. The purpose of this bibliographical guide is to bring together many of the important references to the subject. Relevant references to some related topics are also included. Although this is definitely not a comprehensive bibliography, we hope that it can be a useful tool for researchers in this fast moving area.

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[36]  B. Mandelbrot.  Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis , 1972 .

[37]  Ignacio Rodriguez-Iturbe,et al.  Streamflow simulation: 2. The broken line process as a potential model for hydrologic simulation , 1972 .

[38]  Richard Gisselquist.  A Continuum of Collision Process Limit Theorems , 1973 .

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[42]  H. Oodaira.  The Law of the Iterated Logarithm for Gaussian Processes , 1973 .

[43]  H. McKean.  Geometry of Differential Space , 1973 .

[44]  B. Mandelbrot.  Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier , 1974, Journal of Fluid Mechanics.

[45]  M. Taqqu.  Weak convergence to fractional brownian motion and to the rosenblatt process , 1975, Advances in Applied Probability.

[46]  A more deterministic version of Harris - Spitzer's “Random constant velocity” model for infinite systems of particles , 1975 .

[47]  B. Mandelbrot.  Limit Theorem on the Self-Normalized Range for Weakly and Strongly Dependent Process , 1975 .

[48]  René Carmona,et al.  Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens , 1976 .

[49]  Fractional integrals of stationary processes and the central limit theorem , 1976 .

[50]  T. Kailath,et al.  Orthogonal functionals of independent-increment processes , 1976, IEEE Trans. Inf. Theory.

[51]  G. Maruyama.  Nonlinear functionals of gaussian stationary processes and their applications , 1976 .

[52]  Y. Sinai.  Self-Similar Probability Distributions , 1976 .

[53]  Dennis P. Lettenmaier,et al.  Operational assessment of hydrologic models of long-term persistence , 1977 .

[54]  M. Taqqu.  Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence , 1977 .

[55]  M. T. Greene,et al.  Long-term dependence in common stock returns , 1977 .

[56]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[57]  Tze Leung Lai,et al.  The Law of the Iterated Logarithm and Upper-Lower Class Tests for Partial Sums of Stationary Gaussian Sequences , 1978 .

[58]  A. I. McLeod,et al.  Preservation of the rescaled adjusted range: 1. A reassessment of the Hurst Phenomenon , 1978 .

[59]  Francisco L. S. Gomide,et al.  Markovian inputs and the Hurst phenomenon , 1978 .

[60]  Generation of skewed annual flows using fast fractional Gaussian noise generator , 1978 .

[61]  Volker Enss.  Renormalization group limits for Wick polynomials of Gaussian processes , 1978 .

[62]  M. Taqqu.  A representation for self-similar processes , 1978 .

[63]  K. N. Helland,et al.  The ‘Hurst phenomenon’ in grid turbulence , 1978, Journal of Fluid Mechanics.

[64]  Simeon M. Berman.  A new kind of tightness of probability measures, and its applications to integral functionals of stochastic processes , 1978 .

[65]  M. Cassandro,et al.  Critical point behaviour and probability theory , 1978 .

[66]  F. Hampel.  Modern trends in the theory of robustness 2 , 1978 .

[67]  J. Eckmann,et al.  A renormalization group analysis of the hierarchical model in statistical mechanics , 1978 .

[68]  Uriel Frisch,et al.  A simple dynamical model of intermittent fully developed turbulence , 1978, Journal of Fluid Mechanics.

[69]  J. W. Eberhard,et al.  Excess (1f) noise in metals , 1978 .

[70]  T. L. Malevich,et al.  Stable Limit Distributions for U-Statistics , 1978 .

[71]  Murray Rosenblatt,et al.  Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables , 1979 .

[72]  R. Dobrushin,et al.  Non-central limit theorems for non-linear functional of Gaussian fields , 1979 .

[73]  Myron T. Greene,et al.  The Effect of Long Term Dependence on Risk-Return Models of Common Stocks , 1979, Oper. Res..

[74]  R. Dobrushin.  Gaussian and their Subordinated Self-similar Random Generalized Fields , 1979 .

[75]  Harry Kesten,et al.  A limit theorem related to a new class of self similar processes , 1979 .

[76]  Simeon M. Berman,et al.  High level sojourns for strongly dependent Gaussian processes , 1979 .

[77]  M. Taqqu.  Convergence of integrated processes of arbitrary Hermite rank , 1979 .

[78]  Paul Manneville,et al.  Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems , 1980 .

[79]  G. Kallianpur.  Stochastic Filtering Theory , 1980 .

[80]  S. Cambanis,et al.  Some Path Properties of p-th Order and Symmetric Stable Processes. , 1980 .

[81]  C. Granger.  Long memory relationships and the aggregation of dynamic models , 1980 .

[82]  Donald A. Dawson,et al.  Spatially homogeneous random evolutions , 1980 .

[83]  T. Lai,et al.  Limit theorems for sums of dependent random variables , 1980 .

[84]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[85]  A. Plikusas.  Estimation of cumulants and large deviations for certain nonlinear transformations of a stationary Gaussian process , 1980 .

[86]  Scaling Limits of Generalized Random Processes , 1980 .

[87]  Péter Major,et al.  On the Effect of Collisions on the Motion of an Atom in $R^1$ , 1980 .

[88]  Joel Zinn,et al.  Convergence to a Stable Distribution Via Order Statistics , 1981 .

[89]  D. Surgailis.  On infinitely divisible self-similar random fields , 1981 .

[90]  A. N. Shiryayev,et al.  Martingales: Recent Developments, Results and Applications , 1981 .

[91]  V. Bentkus,et al.  Classes of self-similar random fields , 1981 .

[92]  S. Cambanis,et al.  Linear Problems in Linear Problems in pth Order and Stable Processes , 1981 .

[93]  Michael F. Shlesinger,et al.  Analogs of renormalization group transformations in random processes , 1981 .

[94]  E W Montroll,et al.  Random walks with self-similar clusters. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[95]  V. K. Rohatgi,et al.  Operator self similar stochastic processes in Rd , 1981 .

[96]  Murray Rosenblatt.  Limit theorems for Fourier transforms of functionals of Gaussian sequences , 1981 .

[97]  P. Major.  Limit theorems for non-linear functionals of Gaussian sequences , 1981 .

[98]  A. Plikusas.  Properties of multiple Itô integrals , 1981 .

[99]  H. Künsch.  Thermodynamics and statistical analysis of Gaussian random fields , 1981 .

[100]  Makoto Maejima.  Some sojourn time problems for strongly dependent Gaussian processes , 1981 .

[101]  A. Astrauskas,et al.  Stable self-similar fields , 1982 .

[102]  G. Maruyama,et al.  Applications of the multiplication of the Ito-Wiener expansiors to limit theorems , 1982 .

[103]  Péter Major.  On renormalizing Gaussian fields , 1982 .

[104]  Murad S. Taqqu,et al.  Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables , 1982 .

[105]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[106]  S. Karlin,et al.  Applications of Anova Type Decompositions for Comparisons of Conditional Variance Statistics Including Jackknife Estimates , 1982 .

[107]  C. D. Hardin,et al.  On the spectral representation of symmetric stable processes , 1982 .

[108]  S. Lovejoy.  Area-Perimeter Relation for Rain and Cloud Areas , 1982, Science.

[109]  E. Montroll,et al.  On 1/f noise and other distributions with long tails. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[110]  Donatas Surgailis,et al.  Zones of attraction of self-similar multiple integrals , 1982 .

[111]  Makoto Maejima.  Some limit theorems for sojourn times of strongly dependent Gaussian processes , 1982 .

[112]  David Douglas Engel,et al.  The Multiple Stochastic Integral , 1982 .

[113]  A. Mandelbaum,et al.  Symmetric Statistics, Poisson Point Processes, and Multiple Wiener Integrals , 1983 .

[114]  Makoto Maejima,et al.  A self-similar process with nowhere bounded sample paths , 1983 .

[115]  Shunsuke Sato,et al.  Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation , 1983 .

[116]  Norio Kôno.  Iterated log type strong limit theorems for self-similar processes , 1983 .

[117]  R. Bhattacharya,et al.  THE HURST EFFECT UNDER TRENDS , 1983 .

[118]  P. Major,et al.  Central limit theorems for non-linear functionals of Gaussian fields , 1983 .

[119]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[120]  Masuo Suzuki,et al.  Phase Transition and Fractals , 1983 .

[121]  A. Astrauskas.  Limit theorems for quadratic forms of linear processes , 1983 .

[122]  Norio Kôno.  Approximate upper functions of Gaussian processes , 1983 .

[123]  Daniel Ocone.  Multiple Integral Expansions for Nonlinear Filtering , 1983 .

[124]  Jürg Fröhlich,et al.  Scaling and Self-Similarity in Physics , 1983 .

[125]  W. Woyczynski,et al.  Existence of a double random integral with respect to stable measures , 1983 .

[126]  Sheldon Goldstein,et al.  Stochastic processes originating in deterministic microscopic dynamics , 1983 .

[127]  Herbert Spohn,et al.  Self-diffusion for particles with stochastic collisions in one dimension , 1983 .

[128]  Makoto Maejima,et al.  On a class of self-similar processes , 1983 .

[129]  H. Graf,et al.  Long-range correlations and estimation of the self-similarity parameter , 1983 .

[130]  Convergence of certain nonlinear transformations of a Gaussian sequence to self-similar processes , 1983 .

[131]  George L. O'Brien,et al.  Marginal distributions of self-similar processes with stationary increments , 1983 .

[132]  Reinhard Lang,et al.  Strongly correlated random fields as observed by a random walker , 1983 .

[133]  Murad S. Taqqu,et al.  Infinite variance self-similar processes subordinate to a poisson measure , 1983 .

[134]  A. Astrauskas.  Limit theorems for sums of linearly generated random variables , 1983 .

[135]  Benoit B. Mandelbrot,et al.  Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality , 1984 .

[136]  Herold Dehling,et al.  Invariance principles for von Mises and U-statistics , 1984 .

[137]  Squig sheets and some other squig fractal constructions , 1984 .

[138]  Generalized powers of strongly dependent random variables , 1984 .

[139]  Estimations analytiques concernant le mouvement brownien fractionnaire à plusieurs paramètres , 1984 .

[140]  Murad S. Taqqu,et al.  Invariance Principle for Symmetric Statistics , 1984 .

[141]  Masuo Suzuki.  Finite-Size Scaling for Transient Similarity and Fractals , 1984 .

[142]  Robert M. Burton,et al.  Scaling limits for point random fields , 1984 .

[143]  Simeon M. Berman,et al.  Sojourns of vector Gaussian processes inside and outside spheres , 1984 .

[144]  L. Giraitis.  Asymptotic distribution of spectral estimates of ito-wiener integrals , 1984 .

[145]  Aleksander Weron,et al.  Stable processes and measures; A survey , 1984 .

[146]  Wojbor A. Woyczyński,et al.  Products of random measures, multilinear random forms, and multiple stochastic integrals , 1984 .

[147]  S. Cambanis,et al.  Prediction of stable processes: Spectral and moving average representations , 1984 .

[148]  Sidney I. Resnick,et al.  Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities , 1985 .

[149]  Makoto Maejima.  SOJOURNS OF MULTIDIMENSIONAL GAUSSIAN PROCESSES WITH DEPENDENT COMPONENTS , 1985 .

[150]  Claudia Czado,et al.  A Survey of Functional Laws of the Iterated Logarithm for Self-Similar Processes , 1985 .

[151]  Liudas Giraitis,et al.  CLT and other limit theorems for functionals of Gaussian processes , 1985 .

[152]  Donatas Surgailis,et al.  On the multiple stable integral , 1985 .

[153]  B. Mandelbrot.  Self-Affine Fractals and Fractal Dimension , 1985 .

[154]  George L. O'Brien,et al.  Self-Similar Processes with Stationary Increments Generated by Point Processes , 1985 .

[155]  Asymptotics of particle trajectories in infinite one‐dimensional systems with collisions , 1985 .

[156]  Integer-valued self-similar processes , 1985 .

[157]  Sidney I. Resnick,et al.  More limit theory for the sample correlation function of moving averages , 1985 .

[158]  W. Vervaat.  Sample Path Properties of Self-Similar Processes with Stationary Increments , 1985 .

[159]  J. H. Lou.  Some properties of a special class of self-similar processes , 1985 .

[160]  Stamatis Cambanis,et al.  Convergence of Quadratic Forms in p-Stable Random Variables and Theta sub p-Radonifying Operators. , 1985 .

[161]  M. Taqqu,et al.  Noncentral Limit Theorems for Quadratic Forms in Random Variables Having Long-Range Dependence , 1985 .

[162]  J. Rosinski,et al.  Moment inequalities for real and vector p-stable stochastic integrals , 1985 .

[163]  B. Mandelbrot,et al.  Fractal properties of rain, and a fractal model , 1985 .

[164]  D. B. Cline,et al.  Linear prediction of ARMA processes with infinite variance , 1985 .

[165]  Product stochastic measures, multiple stochastic integrals and their extensions to nuclear space valued processes. Technical report, 1 September 1984-31 August 1985 , 1985 .

[166]  Claudia Czado,et al.  Reproducing Kernel Hilbert Space for Some Non-Gaussian Processes , 1985 .

[167]  Svante Janson,et al.  Remarks on the Foundations of Measures of Dependence. , 1985 .

[168]  J. Szulga,et al.  Random Multilinear Forms , 1986 .

[169]  W. Vervaat,et al.  Stationary Self-Similar Extremal Processes and Random Semicontinuous Functions , 1986 .

[170]  Hausdorff dimension of sample paths for self-similar processes , 1986 .

[171]  A. I. McLeod,et al.  Fractional time series modelling , 1986 .

[172]  D. Surgailis,et al.  Multivariate Appell polynomials and the central limit theorem , 1986 .

[173]  M. Taqqu,et al.  Using Renewal Processes to Generate Long-Range Dependence and High Variability , 1986 .

[174]  Murad S. Taqqu.  Sojourn in an elliptical domain , 1986 .

[175]  Daren B. H. Cline,et al.  Convolution tails, product tails and domains of attraction , 1986 .

[176]  Yuji Kasahara,et al.  Functional limit theorems for weighted sums of I.I.D. random variables , 1986 .

[177]  Jan Rosiński,et al.  On Ito Stochastic Integration with Respect to $p$-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals , 1986 .

[178]  Jan Rosiński,et al.  On stochastic integral representation of stable processes with sample paths in Banach spaces , 1986 .

[179]  Makoto Maejima.  Some sojourn time problems for 2-dimensional Gaussaian processes , 1986 .

[180]  Magda Peligrad,et al.  Recent advances in the central limit theorem and its weak invariance principle for mixing sequences , 1986 .

[181]  Toshio Mori,et al.  The law of the iterated logarithm for self-similar processes represented by multiple wiener integrals , 1986 .

[182]  M. Taqqu,et al.  Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables , 1986 .

[183]  Florin Avram,et al.  Symmetric polynomials of random variables attracted to an infinitely divisible law , 1986 .

[184]  Florin Avram,et al.  Weak Convergence of Moving Averages with Infinite Variance , 1986 .

[185]  M. Taqqu,et al.  Central limit theorems for quadratic forms in random variables having long-range dependence , 1987 .

[186]  Murad S. Taqqu,et al.  Multiple stochastic integrals with dependent integrators , 1987 .

[187]  The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals , 1987 .

[188]  T. Sun,et al.  A central limit theorem for non-instantaneous filters of a stationary Gaussian Process , 1987 .

[189]  Svetlozar T. Rachev,et al.  An Ideal Metric and the Rate of Convergence to a Self-Similar Process , 1987 .

[190]  Stamatis Cambanis,et al.  Innovations and Wold decompositions of stable sequences , 1988 .