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Convergence of Stochastic Processes / David Pollard
| Convergence of Stochastic Processes / David Pollard |
| Autore | Pollard, David |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1984 |
| Descrizione fisica | xiv, 215 p. : ill. ; 24 cm |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60G07 - General theory of stochastic processes [MSC 2020] 60G17 - Sample path properties [MSC 2020] 60F15 - Strong limit theorems [MSC 2020] 60F17 - Functional limit theorems; invariance principles [MSC 2020] 62E20 - Asymptotic distribution theory in statistics [MSC 2020] |
| Soggetto non controllato |
Brownian Motion
Brownian bridge Convergence Gaussian processes Martingales Mathematical statistics Maxima Random functions Statistics Stochastic processes |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0268654 |
Pollard, David
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| New York, : Springer-Verlag, 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Convergence of Stochastic Processes / David Pollard
| Convergence of Stochastic Processes / David Pollard |
| Autore | Pollard, David |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1984 |
| Descrizione fisica | xiv, 215 p. : ill. ; 24 cm |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60F15 - Strong limit theorems [MSC 2020] 60F17 - Functional limit theorems; invariance principles [MSC 2020] 60G07 - General theory of stochastic processes [MSC 2020] 60G17 - Sample path properties [MSC 2020] 62E20 - Asymptotic distribution theory in statistics [MSC 2020] |
| Soggetto non controllato |
Brownian Bridge
Brownian Motion Convergence Gaussian processes Martingales Mathematical statistics Maxima Random functions Statistics Stochastic processes |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts. |
| Record Nr. | UNICAMPANIA-VAN00268654 |
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Pollard, David
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| New York, : Springer-Verlag, 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Decoupling : From Dependence to Independence : Randomly stopped processes, U-statistics and processes, martingales and beyond / Víctor H. de la Peña, Evarist Giné
| Decoupling : From Dependence to Independence : Randomly stopped processes, U-statistics and processes, martingales and beyond / Víctor H. de la Peña, Evarist Giné |
| Autore | Peña, Victor H. de la |
| Pubbl/distr/stampa | New York, : Springer, 1999 |
| Descrizione fisica | xv, 392 p. ; 24 cm |
| Altri autori (Persone) | Giné, Evarist |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60E15 - Inequalities; stochastic orderings [MSC 2020] 60F05 - Central limit and other weak theorems [MSC 2020] 60F15 - Strong limit theorems [MSC 2020] 60F17 - Functional limit theorems; invariance principles [MSC 2020] 60G40 - Stopping times; optimal stopping problems; gambling theory [MSC 2020] 60G42 - Martingales with discrete parameter [MSC 2020] 60G50 - Sums of independent random variables; random walks [MSC 2020] 60Jxx - Markov processes [MSC 2020] 62E20 - Asymptotic distribution theory in statistics [MSC 2020] |
| Soggetto non controllato |
Law of large numbers
Law of the iterated logarithms Martingales Maxima Random Variables Random functions Statistics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00300236 |
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Peña, Victor H. de la
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| New York, : Springer, 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Gaussian Random Functions / by M. A. Lifshits
| Gaussian Random Functions / by M. A. Lifshits |
| Autore | Lifshits, Mikhail A. |
| Pubbl/distr/stampa | Dordrecht, : Springer, : Kluwer, 1995 |
| Descrizione fisica | xi, 333 p. ; 24 cm |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60F10 - Large deviations [MSC 2020] 60G50 - Sums of independent random variables; random walks [MSC 2020] |
| Soggetto non controllato |
Distributions
Gaussian distributions Gaussian measures Law of the iterated logarithms Probability theory Random functions Variance |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00294341 |
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Lifshits, Mikhail A.
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| Dordrecht, : Springer, : Kluwer, 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Gaussian Random Processes / I. A. Ibragimov, Y. A. Rozanov ; Translated by A. B. Aries
| Gaussian Random Processes / I. A. Ibragimov, Y. A. Rozanov ; Translated by A. B. Aries |
| Autore | Ibragimov, Illdar A. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1978 |
| Descrizione fisica | x, 277 p. : ill. ; 24 cm |
| Altri autori (Persone) | Rozanov, Yurii A. |
| Soggetto topico |
60G15 - Gaussian processes [MSC 2020]
60G35 - Signal detection and filtering (aspects of stochastic processes) [MSC 2020] 60G10 - Stationary stochastic processes [MSC 2020] |
| Soggetto non controllato |
Ergodic theory
Gaussian measures Gaussian processes Mixing Probability Measures Random functions Stationary processes |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0268179 |
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Ibragimov, Illdar A.
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| New York, : Springer-Verlag, 1978 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Gaussian Random Processes / I. A. Ibragimov, Y. A. Rozanov ; Translated by A. B. Aries
| Gaussian Random Processes / I. A. Ibragimov, Y. A. Rozanov ; Translated by A. B. Aries |
| Autore | Ibragimov, Illdar A. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1978 |
| Descrizione fisica | x, 277 p. : ill. ; 24 cm |
| Altri autori (Persone) | Rozanov, Yurii A. |
| Soggetto topico |
60G10 - Stationary stochastic processes [MSC 2020]
60G15 - Gaussian processes [MSC 2020] 60G35 - Signal detection and filtering (aspects of stochastic processes) [MSC 2020] |
| Soggetto non controllato |
Ergodic theory
Gaussian measures Gaussian processes Mixing Probability measures Random functions Stationary processes |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes. |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00268179 |
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Ibragimov, Illdar A.
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| New York, : Springer-Verlag, 1978 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Limit theorems for unions of random closed sets / Ilya S. Molchanov
| Limit theorems for unions of random closed sets / Ilya S. Molchanov |
| Autore | Molchanov, Ilya S. |
| Pubbl/distr/stampa | Berlin [etc.], : Springer-Verlag, 1993 |
| Descrizione fisica | x, 157 p. ; 24 cm |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60Dxx - Geometric probability and stochastic geometry [MSC 2020] |
| Soggetto non controllato |
Addition
Random Variables Random functions Random sets Regular variation Set-valued analysis Spatial Statistics Stochastic Geometry |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00290556 |
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Molchanov, Ilya S.
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| Berlin [etc.], : Springer-Verlag, 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Limit theorems for unions of random closed sets / Ilya S. Molchanov
| Limit theorems for unions of random closed sets / Ilya S. Molchanov |
| Autore | Molchanov, Ilya S. |
| Pubbl/distr/stampa | Berlin [etc.], : Springer-Verlag, 1993 |
| Descrizione fisica | x, 157 p. ; 24 cm |
| Soggetto topico |
60-XX - Probability theory and stochastic processes [MSC 2020]
60Dxx - Geometric probability and stochastic geometry [MSC 2020] |
| Soggetto non controllato |
Addition
Random Variables Random functions Random sets Regular variation Set-valued analysis Spatial Statistics Stochastic Geometry |
| ISBN |
03-87573-93-3
35-405-7393-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00049342 |
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Molchanov, Ilya S.
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| Berlin [etc.], : Springer-Verlag, 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Markov Random Fields / Yu. A. Rozanov ; Transl. from the Russian by Constance M. Elson
| Markov Random Fields / Yu. A. Rozanov ; Transl. from the Russian by Constance M. Elson |
| Autore | Rozanov, Yurii A. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1982 |
| Descrizione fisica | ix, 201 p. : ill. ; 24 cm |
| Soggetto topico |
60Jxx - Markov processes [MSC 2020]
60H10 - Stochastic ordinary differential equations [MSC 2020] 60G60 - Random fields [MSC 2020] |
| Soggetto non controllato |
Brownian Motion
Conditional probability Fields Markov property Probability distribution Probability spaces Random fields Random functions Vector probability measure |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN0268531 |
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Rozanov, Yurii A.
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| New York, : Springer-Verlag, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Markov Random Fields / Yu. A. Rozanov ; Transl. from the Russian by Constance M. Elson
| Markov Random Fields / Yu. A. Rozanov ; Transl. from the Russian by Constance M. Elson |
| Autore | Rozanov, Yurii A. |
| Pubbl/distr/stampa | New York, : Springer-Verlag, 1982 |
| Descrizione fisica | ix, 201 p. : ill. ; 24 cm |
| Soggetto topico |
60G60 - Random fields [MSC 2020]
60H10 - Stochastic ordinary differential equations [MSC 2020] 60Jxx - Markov processes [MSC 2020] |
| Soggetto non controllato |
Brownian Motion
Conditional probability Fields Markov property Probability distributions Probability measures Probability spaces Random fields Random functions Vector |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | In this book we study Markov random functions of several variables. What is traditionally meant by the Markov property for a random process (a random function of one time variable) is connected to the concept of the phase state of the process and refers to the independence of the behavior of the process in the future from its behavior in the past, given knowledge of its state at the present moment. Extension to a generalized random process immediately raises nontrivial questions about the definition of a suitable" phase state," so that given the state, future behavior does not depend on past behavior. Attempts to translate the Markov property to random functions of multi-dimensional "time," where the role of "past" and "future" are taken by arbitrary complementary regions in an appro priate multi-dimensional time domain have, until comparatively recently, been carried out only in the framework of isolated examples. How the Markov property should be formulated for generalized random functions of several variables is the principal question in this book. We think that it has been substantially answered by recent results establishing the Markov property for a whole collection of different classes of random functions. These results are interesting for their applications as well as for the theory. In establishing them, we found it useful to introduce a general probability model which we have called a random field. In this book we investigate random fields on continuous time domains. Contents CHAPTER 1 General Facts About Probability Distributions §1. |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00268531 |
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Rozanov, Yurii A.
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| New York, : Springer-Verlag, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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