rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Theory of Stochastic Processes
    sub title: With Applications to Financial Mathematics and Risk Theory
  name:
    name part: Gusak, Dmytro.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kukush, Alexander.
    role:
      role term: author.
  name:
    name part: Kulik, Alexey.
    role:
      role term: author.
  name:
    name part: Mishura, Yuliya.
    role:
      role term: author.
  name:
    name part: Pilipenko, Andrey.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 376 p. 8 illus. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko.
  subject:
    topic: Mathematics
  subject:
    topic: Business mathematics
  subject:
    topic: Actuarial science
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Actuarial Sciences
  subject:
    topic: Business Mathematics
  subject:
    topic: Statistics for Business/Economics/Mathematical Finance/Insurance
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Problem Books in Mathematics
  identifier: 9780387878621
  identifier: http://dx.doi.org/10.1007/978-0-387-87862-1
  record info:
    record creation date: 100710
    record change date: 20151204161424.0
    record identifier: 978-0-387-87862-1