000 04350nam a22005175i 4500
001 978-3-642-39363-1
003 DE-He213
005 20140220082915.0
007 cr nn 008mamaa
008 130716s2013 gw | s |||| 0|eng d
020 _a9783642393631
_9978-3-642-39363-1
024 7 _a10.1007/978-3-642-39363-1
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aGraham, Carl.
_eauthor.
245 1 0 _aStochastic Simulation and Monte Carlo Methods
_h[electronic resource] :
_bMathematical Foundations of Stochastic Simulation /
_cby Carl Graham, Denis Talay.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXVI, 260 p. 4 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStochastic Modelling and Applied Probability,
_x0172-4568 ;
_v68
505 0 _aPart I:Principles of Monte Carlo Methods -- 1.Introduction -- 2.Strong Law of Large Numbers and Monte Carlo Methods -- 3.Non Asymptotic Error Estimates for Monte Carlo Methods -- Part II:Exact and Approximate Simulation of Markov Processes -- 4.Poisson Processes -- 5.Discrete-Space Markov Processes -- 6.Continuous-Space Markov Processes with Jumps -- 7.Discretization of Stochastic Differential Equations -- Part III:Variance Reduction, Girsanov’s Theorem, and Stochastic Algorithms -- 8.Variance Reduction and Stochastic Differential Equations -- 9.Stochastic Algorithms -- References -- Index.
520 _aIn various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view.  The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.  
650 0 _aMathematics.
650 0 _aFinance.
650 0 _aNumerical analysis.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aNumerical Analysis.
650 2 4 _aQuantitative Finance.
700 1 _aTalay, Denis.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642393624
830 0 _aStochastic Modelling and Applied Probability,
_x0172-4568 ;
_v68
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-39363-1
912 _aZDB-2-SMA
999 _c98451
_d98451