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  • 1
    Online Resource
    Online Resource
    Theory of Stochastic Processes : With Applications to Financial Mathematics and Risk Theory (2010)
    New York, NY : Springer-Verlag New York
    Details
    UID:
    gbv_1649893795
    Format: Online-Ressource (XII, 376p. 8 illus, digital)
    Edition: 1
    ISBN: 9780387878621
    Series Statement: Problem Books in Mathematics
    Content: Definition of stochastic process. Cylinder #x03C3;-algebra, finite-dimensional distributions, the Kolmogorov theorem -- Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions -- Trajectories. Modifications. Filtrations -- Continuity. Differentiability. Integrability -- Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures -- Gaussian processes -- Martingales and related processes in discrete and continuous time. Stopping times -- Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values -- Prediction and interpolation -- Markov chains: Discrete and continuous time -- Renewal theory. Queueing theory -- Markov and diffusion processes -- It#x00F4; stochastic integral. It#x00F4; formula. Tanaka formula -- Stochastic differential equations -- Optimal stopping of random sequences and processes -- Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems -- Statistics of stochastic processes -- Stochastic processes in financial mathematics (discrete time) -- Stochastic processes in financial mathematics (continuous time) -- Basic functionals of the risk theory.
    Content: This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory. The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields. The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given. The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions. This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.
    Note: Description based upon print version of record , ""Preface""; ""Contents""; ""Definition of stochastic process. Cylinder -algebra, finite-dimensional distributions, the Kolmogorov theorem""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Trajectories. Modifications. Filtrations""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions"" , ""Continuity. Differentiability. Integrability""""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Gaussian processes""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Martingales and related processes in discrete and continuous time. Stopping times""; ""Theoretical grounds""; ""Bibliography"" , ""Problems""""Hints""; ""Answers and Solutions""; ""Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Prediction and interpolation""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Markov chains: Discrete and continuous time""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Renewal theory. Queueing theory""; ""Theoretical grounds"" , ""Bibliography""""Problems""; ""Hints""; ""Answers and Solutions""; ""Markov and diffusion processes""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""ItÃ? stochastic integral. ItÃ? formula. Tanaka formula""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Stochastic differential equations""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Optimal stopping of random sequences and processes""; ""Theoretical grounds""; ""Bibliography""; ""Problems"" , ""Hints""""Answers and Solutions""; ""Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Statistics of stochastic processes""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Stochastic processes in financial mathematics (discrete time)""; ""Theoretical grounds""; ""Bibliography""; ""Problems""; ""Hints""; ""Answers and Solutions""; ""Stochastic processes in financial mathematics (continuous time)"" , ""Theoretical grounds""
    Additional Edition: ISBN 9780387878614
    Additional Edition: Buchausg. u.d.T. Theory of stochastic processes New York : Springer, 2010 ISBN 9780387878614
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    SK 820
    RVK:
    QH 237
    Keywords: Stochastischer Prozess ; Stochastischer Prozess
    DOI: 10.1007/978-0-387-87862-1
    URL: Volltext  (lizenzpflichtig)
    URL: Volltext  (lizenzpflichtig)
    URL: Kapitel 1
    URL: Einführung/Vorwort
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
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  • 2
    Online Resource
    Online Resource
    On the Use of Stochastic Processes in Modeling Reliability Problems (1985)
    Berlin, Heidelberg : Springer Berlin Heidelberg
    Details
    UID:
    b3kat_BV046871839
    Format: 1 Online-Ressource (VI, 105 p)
    Edition: 1st ed. 1985
    ISBN: 9783642465536
    Series Statement: Lecture Notes in Economics and Mathematical Systems 252
    Content: Stochastic processes are powerful tools for the investigation of reliability and availability of repairable equipment and systems. Because of the involved models, and in order to be mathematically tractable, these processes are generally confined to the class of regenerative stochastic processes with a finite state space, to which belong: renewal processes, Markov processes, semi-Markov processes, and more general regenerative processes with only one (or a few) regeneration staters). The object of this monograph is to review these processes and to use them in solving some reliability problems encountered in practical applications. Emphasis is given to a comprehensive exposition of the analytical procedures, to the limitations in­ volved, and to the unification and extension of. the models known in the literature. The models investigated here assume. that systems have only one repair crew and that no further failure can occur at system down. Repair and failure rates are general­ ized step-by-step, up to the case in which the involved process is regenerative with only one (or a few) regeneration state(s). Investigations deal with different kinds of reliabilities and availabilities for series/parallel structures. Preventive main­ tenance and imperfect switching are considered in some examples
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783540156994
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783642465543
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    QH 237
    RVK:
    SI 853
    Keywords: Mathematisches Modell ; Reliabilität ; Stochastischer Prozess ; Stochastischer Prozess ; Zuverlässigkeit ; Zuverlässigkeitstheorie ; Stochastischer Prozess ; Betriebssicherheit ; Hochschulschrift
    DOI: 10.1007/978-3-642-46553-6
    URL: Volltext  (URL des Erstveröffentlichers)
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  • 3
    Online Resource
    Online Resource
    Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness (2002)
    Berlin [u.a.] : Springer
    Details
    UID:
    gbv_165530755X
    Format: Online-Ressource
    Edition: [Online-Ressource]
    Edition: Berlin [u.a.] Springer
    ISBN: 9783540446231
    Series Statement: Lecture notes in mathematics 1766
    Content: General Facts About The Method Purpose Of The Paper -- The Central Limit Theorems For Markov Chains Theorems A, B, C -- Quasi-Compact Operators of Diagonal Type And Their Perturbations -- First Properties of Fourier Kernels Application -- Peripheral Eigenvalues of Fourier Kernels -- Proofs Of Theorems A, B, C -- Renewal Theorem For Markov Chains Theorem D -- Large Deviations For Markov Chains Theorem E -- Ergodic Properties For Markov Chains -- Markov Chains Associated With Lipschitz Kernels Examples -- Stochastic Properties Of Dynamical Systems Theorems A*, B*, C*, D*, E* -- Expanding Maps -- Proofs Of Some Statements In Probability Theory -- Functional Analysis Results On Quasi-Compactness -- Generalization To The Non-Ergodic Case.
    Content: The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
    Note: Lizenzpflichtig
    Additional Edition: ISBN 9783540424154
    Additional Edition: Druckausg. Hennion, Hubert Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness Berlin : Springer, 2001 ISBN 3540424156
    Language: English
    Subjects: Mathematics
    RVK:
    SI 850
    Keywords: Markov-Kette ; Grenzwertsatz ; Dynamisches System ; Stochastischer Prozess ; Markov-Kette ; Grenzwertsatz ; Stochastischer Prozess ; Dynamisches System
    DOI: 10.1007/b87874
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
    URL: Kapitel 1
    URL: Inhaltsverzeichnis
    URL: Cover
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  • 4
    Online Resource
    Online Resource
    Random Perturbation Methods with Applications in Science and Engineering (2002)
    New York, NY : Springer New York
    Details
    UID:
    b3kat_BV042419026
    Format: 1 Online-Ressource (XII, 490 p)
    ISBN: 9780387224466 , 9781468492712
    Series Statement: Applied Mathematical Sciences 150
    Note: As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems
    Language: English
    Keywords: Dynamisches System ; Störungstheorie ; Stochastischer Prozess
    DOI: 10.1007/b98905
    URL: Volltext
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  • 5
    Online Resource
    Online Resource
    Stochastic Ordering and Dependence in Applied Probability (1995)
    New York, NY : Springer New York
    Details
    UID:
    b3kat_BV042420038
    Format: 1 Online-Ressource (VIII, 194p)
    ISBN: 9781461225287 , 9780387944500
    Series Statement: Lecture Notes in Statistics 97
    Note: This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen­ sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re­ newal processes, then results on stochastic ordering of networks, re~~ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem­ plified by results on queueing networks and point processes among others
    Language: English
    Keywords: Stochastische Ordnung ; Wahrscheinlichkeit ; Stochastischer Prozess ; Ordnungsstatistik ; Stochastische Abhängigkeit
    DOI: 10.1007/978-1-4612-2528-7
    URL: Volltext
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