Author: Volker Mayer
Publisher: Springer
ISBN: 3642236502
Category : Mathematics
Languages : en
Pages : 122
Book Description
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.
Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
Author: Volker Mayer
Publisher: Springer Science & Business Media
ISBN: 3642236499
Category : Mathematics
Languages : en
Pages : 122
Book Description
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.
Publisher: Springer Science & Business Media
ISBN: 3642236499
Category : Mathematics
Languages : en
Pages : 122
Book Description
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.
Random Mappings
Author: Valentin Fedorovich Kolchin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 232
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 232
Book Description
Random Mappings
Author: V. F. Kolchin
Publisher: Springer
ISBN: 9780387961545
Category : Mathematics
Languages : en
Pages : 206
Book Description
Publisher: Springer
ISBN: 9780387961545
Category : Mathematics
Languages : en
Pages : 206
Book Description
Identification Problem and Random Contraction Mappings
Author: Kandarp Oza
Publisher:
ISBN:
Category :
Languages : en
Pages : 338
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 338
Book Description
Random Finite Sets for Robot Mapping & SLAM
Author: John Stephen Mullane
Publisher: Springer Science & Business Media
ISBN: 3642213898
Category : Technology & Engineering
Languages : en
Pages : 161
Book Description
The monograph written by John Mullane, Ba-Ngu Vo, Martin Adams and Ba-Tuong Vo is devoted to the field of autonomous robot systems, which have been receiving a great deal of attention by the research community in the latest few years. The contents are focused on the problem of representing the environment and its uncertainty in terms of feature based maps. Random Finite Sets are adopted as the fundamental tool to represent a map, and a general framework is proposed for feature management, data association and state estimation. The approaches are tested in a number of experiments on both ground based and marine based facilities.
Publisher: Springer Science & Business Media
ISBN: 3642213898
Category : Technology & Engineering
Languages : en
Pages : 161
Book Description
The monograph written by John Mullane, Ba-Ngu Vo, Martin Adams and Ba-Tuong Vo is devoted to the field of autonomous robot systems, which have been receiving a great deal of attention by the research community in the latest few years. The contents are focused on the problem of representing the environment and its uncertainty in terms of feature based maps. Random Finite Sets are adopted as the fundamental tool to represent a map, and a general framework is proposed for feature management, data association and state estimation. The approaches are tested in a number of experiments on both ground based and marine based facilities.
Stochastics
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter
ISBN: 3110206765
Category : Mathematics
Languages : en
Pages : 381
Book Description
This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.
Publisher: Walter de Gruyter
ISBN: 3110206765
Category : Mathematics
Languages : en
Pages : 381
Book Description
This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.
Combinatorial Stochastic Processes
Author: Jim Pitman
Publisher: Springer Science & Business Media
ISBN: 354030990X
Category : Mathematics
Languages : en
Pages : 257
Book Description
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Publisher: Springer Science & Business Media
ISBN: 354030990X
Category : Mathematics
Languages : en
Pages : 257
Book Description
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Random Mappings
Author: Valentin F. Kolčin
Publisher:
ISBN: 9783540961543
Category : Combinatorial probabilities
Languages : en
Pages : 206
Book Description
Publisher:
ISBN: 9783540961543
Category : Combinatorial probabilities
Languages : en
Pages : 206
Book Description
Probabilistic Problems of Discrete Mathematics
Author: Valentin Fedorovich Kolchin
Publisher: American Mathematical Soc.
ISBN: 9780821831236
Category : Mathematics
Languages : en
Pages : 228
Book Description
Publisher: American Mathematical Soc.
ISBN: 9780821831236
Category : Mathematics
Languages : en
Pages : 228
Book Description
The mapping problem in coarse-grained modelling of biomolecules
Author:
Publisher: Marco Giulini
ISBN:
Category : Science
Languages : en
Pages : 174
Book Description
Publisher: Marco Giulini
ISBN:
Category : Science
Languages : en
Pages : 174
Book Description