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E-raamat: Simulation of Stochastic Processes with Given Accuracy and Reliability

(Associated Professor, Department of Mathematical Analysis, Uzhhorod National University, Ukraine), (Associated Professor, Depart), (Professor, Taras Shevchenko National University of Kyiv, Faculty of Mathematics and Mechanics, Ukraine),
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  • Ilmumisaeg: 22-Nov-2016
  • Kirjastus: ISTE Press Ltd - Elsevier Inc
  • Keel: eng
  • ISBN-13: 9780081020852
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Simulation of Stochastic Processes with Given Accuracy and ReliabilitySuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 22-Nov-2016
  • Kirjastus: ISTE Press Ltd - Elsevier Inc
  • Keel: eng
  • ISBN-13: 9780081020852
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Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of constructed models. By outlining the new approaches and modern methods of simulation of stochastic processes, this book provides methods and tools in measuring accuracy and reliability in functional spaces. The authors explore analysis of the theory of Sub-Gaussian (including Gaussian one) and Square Gaussian random variables and processes and Cox processes.  Methods of simulation of stochastic processes and fields with given accuracy and reliability in some Banach spaces are also considered.

Arvustused

"The book will be useful both for mathematicians and practitioners who deal with stochastic models. It contains rigorous formulas together with simulation results. The mathematical level of the book is high, however it is accessible for everybody who is interested in approximations of stochastic processes." --Zentralblatt MATH 1376

Muu info

Outlines new approaches and modern methods of simulation of stochastic processes with given accuracy and reliability in functional spaces
Introduction ix
Chapter 1 The Distribution of the Estimates for the Norm of Sub-Gaussian Stochastic Processes
1(70)
1.1 The space of sub-Gaussian random variables and sub-Gaussian stochastic processes
2(13)
1.1.1 Exponential moments of sub-Gaussian random variables
8(1)
1.1.2 The sum of independent sub-Gaussian random variables
9(1)
1.1.3 Sub-Gaussian stochastic processes
10(5)
1.2 The space of strictly sub-Gaussian random variables and strictly sub-Gaussian stochastic processes
15(9)
1.2.1 Strictly sub-Gaussian stochastic processes
22(2)
1.3 The estimates of convergence rates of strictly sub-Gaussian random series in L2(T)
24(4)
1.4 The distribution estimates of the norm of sub-Gaussian stochastic processes in Lp(T)
28(2)
1.5 The distribution estimates of the norm of sub-Gaussian stochastic processes in some Orlicz spaces
30(4)
1.6 Convergence rate estimates of strictly sub-Gaussian random series in Orlicz spaces
34(8)
1.7 Strictly sub-Gaussian random series with uncorrected or orthogonal items
42(6)
1.8 Uniform convergence estimates of sub-Gaussian random series
48(10)
1.9 Convergence estimate of strictly sub-Gaussian random series in C(T)
58(11)
1.10 The estimate of the norm distribution of Lp-processes
69(2)
Chapter 2 Simulation of Stochastic Processes Presented in the Form of Series
71(34)
2.1 General approaches for model construction of stochastic processes
71(2)
2.2 Karhunen--Loeve expansion technique for simulation of stochastic processes
73(11)
2.2.1 Karhunen--Loeve model of strictly sub-Gaussian stochastic processes
74(1)
2.2.2 Accuracy and reliability of the KL model in L2(T)
75(1)
2.2.3 Accuracy and reliability of the KL model in LP(T), p > 0
75(2)
2.2.4 Accuracy and reliability of the KL model in LU(T)
77(2)
2.2.5 Accuracy and reliability of the KL model in C(T)
79(5)
2.3 Fourier expansion technique for simulation of stochastic processes
84(9)
2.3.1 Fourier model of strictly sub-Gaussian stochastic process
85(1)
2.3.2 Accuracy and reliability of the F-model in L2(T)
85(1)
2.3.3 Accuracy and reliability of the F-model in Lp(T), p > 0
86(2)
2.3.4 Accuracy and reliability of the F-model in LU(T)
88(2)
2.3.5 Accuracy and reliability of the F-model in C(T)
90(3)
2.4 Simulation of stationary stochastic process with discrete spectrum
93(9)
2.4.1 The model of strictly sub-Gaussian stationary process with discrete spectrum
94(1)
2.4.2 Accuracy and reliability of the D(T)-model in L2(T)
95(1)
2.4.3 Accuracy and reliability of the D(T)-model in Lp(T), p > 0
95(2)
2.4.4 Accuracy and reliability of the D(T)-model in LU(T)
97(4)
2.4.5 Accuracy and reliability of the D(T)-model in C(T)
101(1)
2.5 Application of Fourier expansion to simulation of stationary stochastic processes
102(3)
2.5.1 The model of a stationary process in which a correlation function can be represented in the form of a Fourier series with positive coefficients
103(2)
Chapter 3 Simulation of Gaussian Stochastic Processes with Respect to Output Processes of the System
105(64)
3.1 The inequalities for the exponential moments of the quadratic forms of Gaussian random variables
107(9)
3.2 The space of square-Gaussian random variables and square-Gaussian stochastic processes
116(1)
3.3 The distribution of supremums of square-Gaussian stochastic processes
117(9)
3.4 The estimations of distribution for supremum of square-Gaussian stochastic processes in the space [ 0, T]d
126(7)
3.5 Accuracy and reliability of simulation of Gaussian stochastic processes with respect to the output process of some system
133(11)
3.6 Model construction of stationary Gaussian stochastic process with discrete spectrum with respect to output process
144(13)
3.7 Simulation of Gaussian stochastic fields
157(12)
3.7.1 Simulation of Gaussian fields on spheres
161(8)
Chapter 4 The Construction of the Model of Gaussian Stationary Processes
169(12)
Chapter 5 The Modeling of Gaussian Stationary Random Processes with a Certain Accuracy and Reliability
181(70)
5.1 Reliability and accuracy in Lp(T), p ≥ 1 of the models for Gaussian stationary random processes
181(21)
5.1.1 The accuracy of modeling stationary Gaussian processes in Lp([ 0, T]), 1 ≤ p ≤ 2
182(6)
5.1.2 The accuracy of modeling stationary Gaussian processes Lp([ 0, T]) at p ≥ 1
188(11)
5.1.3 The accuracy of modeling Gaussian stationary random processes in norms of Orlicz spaces
199(3)
5.2 The accuracy and reliability of the model stationary random processes in the uniform metric
202(20)
5.2.1 The accuracy of simulation of stationary Gaussian processes with bounded spectrum
202(11)
5.2.2 Application of Lp(Ω) - processes theory in simulation of Gaussian stationary random processes
213(9)
5.3 Application of Subφ (Ω) space theory to find the accuracy of modeling for stationary Gaussian processes
222(19)
5.4 Generalized model of Gaussian stationary processes
241(10)
Chapter 6 Simulation of Cox Random Processes
251(54)
6.1 Random Cox processes
251(2)
6.2 Simulation of log Gaussian Cox processes as a demand arrival process in actuarial mathematics
253(15)
6.3 Simplified method of simulating log Gaussian Cox processes
268(12)
6.4 Simulation of the Cox process when density is generated by a homogeneous log Gaussian field
280(6)
6.5 Simulation of log Gaussian Cox process when the density is generated by the inhomogeneous field
286(6)
6.6 Simulation of the Cox process when the density is generated by the square Gaussian random process
292(7)
6.7 Simulation of the square Gaussian Cox process when density is generated by a homogeneous field
299(2)
6.8 Simulation of the square Gaussian Cox process when the density is generated by an inhomogeneous field
301(4)
Chapter 7 On the Modeling of Gaussian Stationary Processes with Absolutely Continuous Spectrum
305(10)
Chapter 8 Simulation of Gaussian Isotropic Random Fields on a Sphere
315(10)
8.1 Simulation of random field with given accuracy and reliability in L2(Sn)
323(1)
8.2 Simulation of random field with given accuracy and reliability in Lp(Sn), p ≥ 2
324(1)
Bibliography 325(8)
Index 333
Yuriy Kozachenko is Professor at Taras Shevchenko National University of Kyiv, Ukraine.Doctor of Sciences in Physics and Mathematics, Laureate of the State Prize of Ukraine in Science and TechnologyMain scientific research interests relate to the study of the properties of random processes in various functional spaces, simulation and statistics of random processes, the theory of wavelet expansions of random processes. One of the founders of the theory of sub-Gaussian and -subGaussian random processes, random processes from Orlicz spaces. Determination of accuracy and reliability of computer simulation of random processes.Author of over 300 scientific papers, several textbooks and seven monographs. Associate professor at Department of Department of Probability Theory and Mathematical Analysis, UzhNU from 2008;Her scientific interests are in the field of simulation of point stochastic processes and fields with given accuracy and reliability, e.g. Cox Processes driven by random intensity, analytical properties of point processes and fields. Author of more than 10 papers. Associate professor at Department of Applied Statistics, TSNUK, Ukraine from 2011.Her scientific interests are in the field of simulation of stochastic processes and fields with given accuracy and reliability in different Banach spaces, analytical properties of stochastic processes and fields; survey statistics. Author of more than 40 papers. Associate professor at Department of Applied Statistics, from 2011.Her scientific interests are in the field of simulation of stochastic processes and fields with given accuracy and reliability in different Banach spaces, analytical properties of stochastic processes and fields; survey statistics. Author of more than 20 papers
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