M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In E. Eberlain and M. S. Taqqu, editors, Dependence in Probability and Statistics, 137--165. Basel:Birkhauser, 1985. (p 38)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1. 5 2 Identities for scalar self similar processes Recall that a real or vector valued process (X t ; t 0) is called self similar for a 2 R if for every c 0 (X ct ; t 0) c X t ; t 0) 2.1) Such processes were studied by Lamperti [20, 21] who called them semi stable. See [34] for a survey of the literature of these processes. The conditioning formula (1.2) for any 0 self similar process ( t ; t 0) is an immediate consequence of the following identity. To see the direct implication, take X(t; to equal 1 (0;1) t) Proposition 2.1 (Pitman and Yor [30] Let (X ....

M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137-162. Birkhauser (Basel, Boston), 1986.

....II. SELF SIMILAR MODELS Self similar processes can briefly be described by their characteristic of being scale invariant. A perfectly self similar process on average looks exactly the same regardless of the time scale observed. A wealth of literature on self similar phenomena has been indexed in [9]. The degree of self similarity of a process is typically described by the Hurst parameter (H) H is between 0.5 and 1.0, where 0.5 represents non self similar behavior and the closer to 1.0, the more long range dependent the process is. A continuous time stochastic process X(t) is then ....

Taqqu, M. A bibliographical guide to self-similar processes and long-range dependence. In E. Eberlein and M. S. Taqqu, editors, Dependence in Probability and Statistics, pages 137-- 165. Birkhauser, 1985.

....observed and categorized by Mandelbrot et al. in the early 1960 s, when describing such diverse natural occurrences as mountain landscapes, earthquake frequency, river flow fluctuations, and errors in communication channels. A wealth of literature on self similar phenomena has been indexed in [Taq85] 35 4.1.1 Definitions The degree of self similarity of a process is typically described by the Hurst parameter (H) named after a hydrologist who spent his life studying the self similar nature of water levels of the Nile river. H is usually between 0.5 and 1.0, where 0.5 represents non ....

Taqqu, M. A bibliographical guide to self-similar processes and long-range dependance. In E. Eberlein and M. S. Taqqu, editors, Dependence in Probability and Statistics, pages 137--165. Birkhauser, 1985.

....[2] for a general treatment of random closed subsets of R I . A real or vector valued process (X t ; t 0) is called fi self similar where fi 2 R I if for every c 0 (X ct ; t 0) d = c fi X t ; t 0) 20) Such processes were studied by Lamperti [24, 25] who called them semistable. See [40] for a survey of the literature of these processes. A random closed subset Z of R I is self similar in the sense (6) iff its age process is 1 selfsimilar. A natural example of a self similar random closed subset of (0; 1) is provided by the closure of the zero set of a fi self similar process for ....

M. S. Taqqu. A bibliographical guide to self-similar processes and longrange dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137--162. Birkhauser (Basel, Boston), 1986.

....2 Identities for scalar self similar processes Recall that a real or vector valued process (X t ; t 0) is called fi self similar for a fi 2 R if for every c 0 (X ct ; t 0) d = c fi X t ; t 0) 2.1) Such processes were studied by Lamperti [21, 22] who called them semi stable. See [35] for a survey of the literature of these processes. The conditioning formula (1.2) for any 0 self similar process ( Theta t ; t 0) is an immediate consequence of the following identity. To see the direct implication, take X(t; to equal 1 (0;1) t) Proposition 2.1 (Pitman and Yor [31] ....

M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137--162. Birkhauser (Basel, Boston), 1986.

....and Section 7 generalizes some of the results of Knight [21] and Pitman Yor [30] See also [8, 9] for some further applications of the results of this paper. 2 Bridges and Excursions of a self similar Markov process. Recall that for fi 2 R a process B : B t ; t 0) is called fi self similar [23, 24, 41, 38] if B has the scaling property (B ct ; t 0) d = c fi B t ; t 0) for each c 0, 13) which generalizes the well known scaling property of Brownian motion for fi = 1 2 . We sometimes write B(t) instead of B t for typographical convenience. Suppose in this section that B is a real or ....

M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137--162. Birkhauser (Basel, Boston), 1986.

....for scalar self similar processes Recall that a real or vector valued process (X t ; t 0) is called fi self similar for a fi 2 R if for every c 0 (X ct ; t 0) d = c fi X t ; t 0) 2.1) selfsimdef Such processes were studied by Lamperti [21, 22] who called them semi stable. See [35] for a survey of the literature of these processes. The conditioning formula (1.2) for any 0 self similar process ( Theta t ; t 0) is an immediate consequence of the following identity To see the direct implication, take X(t; to equal 1 (0;1) t) Proposition 2.1 (Pitman and Yor [31] Let ....

M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137--162. Birkhauser (Basel, Boston), 1986.

....prove useful in other contexts. The following theorem presents the conclusion of this argument in a fairly general setting. Recall that a real or vector valued process (X t ; t 0) is called fi self similar for some fi 2 R if for every c 0 (X ct ; t 0) d = c fi X t ; t 0) 24) See [20] for a survey of the literature of these processes. Note that (X t ) is fi self similar iff the process (Y t ) defined by Y t = t Gammafi X t is 0 self similar, that is to say, for every c 0 (Y ct ; t 0) d = Y t ; t 0) 25) This definition of 0 self similarity makes sense even for Y ....

M. S. Taqqu. A bibliographical guide to self-similar processes and longrange dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137--162. Birkhauser (Basel, Boston), 1986.

....be more in the uncertainty about the estimate, which, taking into account the long memory character of the process, would be larger. Beran (1994a) is a good introduction to the Statistics of long memory processes. From a more probabilistic point of view, a bibliography, up to 1985, is contained in Taqqu (1986). Recently the Journal of Econometrics has published a special issue entirely devoted to fractional differencing and long memory processes (Baillie and King (1996) 1.2 Mathematical preliminaries and notations. In this Section we recall some well known facts about a second order stationary ....

Taqqu, M. S. (1986). A bibliographical guide to self-similar processes and long-range dependence, in E. Eberlein and M. S. Taqqu (eds), Dependence in Probability and Statistics, Birkhauser, Boston.

....descriptors. A summary of fractal techniques has been presented by Kinsner [32] Self similarity refers to the property of an object to maintain certain characteristics when observed at different scales. The concepts of longterm dependency and self similarity have been extensively studied by Taqqu [39]. Addie et al. 20] proposed the use of the term fractality in the sense that the autocovariance of the traffic exhibits selfsimilarity. Other self similar models include fractional ARIMA processes (Grange and Joyeux [27] Self similar models have been applied in variablebit rate (VBR) video ....

M. Taqqu, "A bibliographical guide to self-similar processes and long-range dependence", in Dependence in Probability and Statistic, E. Eberlein and M. Taqqu (Eds.), Birkhaeuser, Basel, pp. 137-165, 1985.

.... has appeared on the subject in the last two decades the interest in self similar processes being generated by their fractal type behavior and by their common usage as stochastic models with long range dependence, beginning with Mandelbrot and van Ness [MV68] An extensive survey is in Taqqu [Taq86] and for a more recent information the reader can consult Chapters 7 and 8 in Samorodnitsky and Taqqu [ST94] We will use the standard notation of H sssi for an H self similar process with stationary increments. A very important class of heavy tailed H sssi processes is that of symmetric ....

M.S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In E. Eberlein and M.S. Taqqu, editors, Dependence in Probability and Statistics, pages 137--162, Boston, 1986. Birkhauser.

No context found.

M.S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In E. Eberlein and M.S. Taqqu, editors, Dependence in Probability and Statistics, pages 137--162, Boston, 1986. Birkhauser.

....individually exhibits characteristics that cover a wide range of time scales. The Noah Effect is synonymous with the infinite variance syndrome the empirical observation that many naturally occurring phenomena can be well described using distributions with infinite variance (for references, see [44, 42, 54]) Mathematically, we use heavy tailed distributions with infinite variance (e.g. Pareto or truncated stable distributions) to account for the Noah Effect, and the parameter ff describing the heaviness of the tail of such a distribution gives a measure of the intensity of the Noah Effect. We ....

M. S. Taqqu. A Bibliographical Guide to Self-Similar Processes and Long-Range Dependence. In E. Eberlein and M. S. Taqqu, editors, Dependence in Probability and Statistics, pages 137--162, Boston, 1986. Birkhauser.

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M. S. Taqqu, "A Bibliographical Guide to Self-Similar Processes and Long-Range Dependence", in: Dependence in Probability and Statistic, E. Eberlein and M. S. Taqqu (Eds.), Birkhauser, Basel, 137-165, 1985.

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M. S. Taqqu, "A Bibliographical Guide to Self-Similar Processes and Long-Range Dependence", in: Dependence in Probability and Statistics, E. Eberlein and M. S. Taqqu (Eds.), Birkhauser, Basel, 137-165, 1985.

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M. S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In E. Eberlain and M. S. Taqqu, editors, Dependence in Probability and Statistics, 137--165. Basel:Birkhauser, 1985. (p 38)

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Taqqu, M.S. : A bibliographical guide to self-similar processes and long-range dependence, in: E. Eberlein and M. Taqqu, eds., Dependence in Probability and Statistics (Birkhauser, Boston, 1986) 137-162.

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M. S. Taqqu, \A Bibliographical Guide to Self-Similar Processes and Long-Range Dependence," in Dependence in Probability and Statistics, E. Eberlein and M. S. Taqqu, eds., pp. 137-165, Birkhauser, Boston, 1985.

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Taqqu, M.S. (1989) . A bibliographical guide to self-similar processes and longrange dependence. In : Eberlein E. and Taqqu, M.S. (eds.) Dependence in Probability and Statistics, 137--162. Birkhauser.

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