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007 cr nn 008mamaa
008 100710s2010 xxu| s |||| 0|eng d
020 _a9780387878621
_9978-0-387-87862-1
040 _cMX-MeUAM
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
082 0 4 _a519.2
_223
100 1 _aGusak, Dmytro.
_eauthor.
245 1 0 _aTheory of Stochastic Processes
_h[recurso electrónico] :
_bWith Applications to Financial Mathematics and Risk Theory /
_cby Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _aXII, 376p. 8 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProblem Books in Mathematics,
_x0941-3502
505 0 _aDefinition of stochastic process. Cylinder s-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 -- Itô stochastic integral. Itô 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 0 _aEconomics
_xStatistics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aStatistics for Business/Economics/Mathematical Finance/Insurance.
700 1 _aKukush, Alexander.
_eauthor.
700 1 _aKulik, Alexey.
_eauthor.
700 1 _aMishura, Yuliya.
_eauthor.
700 1 _aPilipenko, Andrey.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387878614
830 0 _aProblem Books in Mathematics,
_x0941-3502
856 4 0 _zLibro electrónico
_uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-387-87862-1
596 _a19
942 _cLIBRO_ELEC
999 _c198191
_d198191