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001 280861
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008 150903s2010 xxu| o |||| 0|eng d
020 _a9780387878621
_99780387878621
024 7 _a10.1007/9780387878621
_2doi
035 _avtls000333203
039 9 _a201509030800
_bVLOAD
_c201404130354
_dVLOAD
_c201404092143
_dVLOAD
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_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA273.A1-274.9
100 1 _aGusak, Dmytro.
_eautor
_9306085
245 1 0 _aTheory of Stochastic Processes :
_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, 376 páginas 8 ilustraciones
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aProblem Books in Mathematics,
_x0941-3502
500 _aSpringer eBooks
505 0 _aDefinition of stochastic process. Cylinder ?-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.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aKukush, Alexander.
_eautor
_9306086
700 1 _aKulik, Alexey.
_eautor
_9306087
700 1 _aMishura, Yuliya.
_eautor
_9306088
700 1 _aPilipenko, Andrey.
_eautor
_9306089
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780387878614
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-387-87862-1
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c280861
_d280861