scispace - formally typeset
Search or ask a question
Author

Donatas Surgailis

Bio: Donatas Surgailis is an academic researcher from Vilnius University. The author has contributed to research in topics: Estimator & Moving average. The author has an hindex of 34, co-authored 144 publications receiving 3907 citations. Previous affiliations of Donatas Surgailis include University of North Carolina at Chapel Hill & Michigan State University.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [1] and Fox and Taqqu [3] for Gaussian variables.
Abstract: A central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [1] and Fox and Taqqu [3] for Gaussian variables. The theorem is applied to prove asymptotical normality of Whittle's estimate of the parameter of strongly dependent linear sequences.

384 citations

Book
27 Apr 2012
TL;DR: Introduction Estimation Some Inference Problems Residual Empirical Processes Regression Models Nonparametric Regression with Heteroscedastic Errors Model Checking under Long Memory Long Memory under Infinite Variance.
Abstract: Introduction Estimation Some Inference Problems Residual Empirical Processes Regression Models Nonparametric Regression with Heteroscedastic Errors Model Checking under Long Memory Long Memory under Infinite Variance.

262 citations

Journal ArticleDOI
TL;DR: Conditions for the CLT for non-linear functionals of stationary Gaussian sequences are discussed, with special references to the borderline between the CLTs and the non-CLTs as discussed by the authors.
Abstract: Conditions for the CLT for non-linear functionals of stationary Gaussian sequences are discussed, with special references to the borderline between the CLT and the non-CLT. Examples of the non-CLT for such functionals with the norming factor $$\sqrt N $$ are given.

221 citations

Journal ArticleDOI
TL;DR: In this article, Surgailis et al. considered the multidimensional case of convergence to self-similar fields and gave a short survey of the separate sections of the paper, including the connection of this theorem with the result of Dobrushin-Major [8] and some similar questions.
Abstract: ZONES OF ATTRACTION OF SELF-SIMILAR MULTIPLE INTEGRALS D. Surgailis UDC 519.21 The goal of this paper is the proof of the theorem announced in [20]. Here we consider the "multidimensional case," i.e., convergence to self-similar fields. We give a short survey of the separate sections. In Sec. 1 the concepts needed are formulated as well as the basic result of the paper (Theorem i). The connection of this theorem with the result of Dobrushin-Major [8] is discussed as well as some similar questions. In Sec. 2 the term making the basic contribution to the distribution of the sums considered is isolated. Here we explain the idea of the following proof, which is broken up into several lemmas, and their formulations are given. The proofs of these lemmas (except for Lemma 5) are carried out to section 3. In section 4 there is proved a lemma (Lemma 1 of [20]) on the convergence with respect to distribution of "discrete multiple integrals" to "continuous" integrals of Ito-- Wiener. With the help of this lemma, the remaining Lemma 5 is proved. i. Notation for what follows: R d is d-dimensional Euclidean space, x.y, ]xl are respectively the scalar product and norm in R d, Z d is the integer-valued d-dimensional lattice. We shall write

122 citations

Journal ArticleDOI
TL;DR: In this article, a probabilistic model of strong initial fluctuations (a zero-range shot-noise field with high amplitudes) is presented, which reveals an intermittent large time behaviour, with the velocity of the largest initial fluctuation determined by the position of the large initial fluctuations (discounted by the heat kernel).
Abstract: The model of the potential turbulence described by the 3-dimensional Burgers' equation with random initial data was developped by Zeldovich and Shandarin, in order to explain the existing Large Scale Structure of the Universe. Most of the recent probabilistic investigations of large time asymptotics of the solution deal with the central limit type results (the “Gaussian scenario”), under suitable moment assumptions on the initial velocity field. These results and some open questions are discussed in Sect. 2, where we concentrate on the Gaussian model and the shot-noise model. In Sect. 3 we construct a probabilistic model of strong initial fluctuations (a zero-range shot-noise field with “high” amplitudes) which reveals an intermittent large time behaviour, with the velocity\(\vec v(t,x)\) determined by the position of the largest initial fluctuation (discounted by the heat kernelg(t,x·)) in a neighborhood ofx. The asymptoties of such local maximum ast→∞ can be analyzed with the help of the theory of records (Sect. 4). Finally, in Sect. 5 we introduce a global definition of a point process oft-local maxima, and show the weak convergence of the suitably rescaled process to a non-trivial limit ast→∞.

102 citations


Cited by
More filters
Journal ArticleDOI

6,278 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Book ChapterDOI
01 Jan 2011
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

3,554 citations

Journal ArticleDOI
TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.
Abstract: (2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.

2,729 citations