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008 | 100710s2010 xxu| s |||| 0|eng d | ||
020 |
_a9780387878621 _9978-0-387-87862-1 |
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
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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 |