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Kloeden P/, Platen E., Schurz H. — Numerical solution of SDE through computer experiments
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Название: Numerical solution of SDE through computer experimentsАвторы: Kloeden P/, Platen E., Schurz H.Аннотация: The book provides an easily accessible computationally oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations in their own fields. Furthermore, it creates an intuitive understanding of the necessary theoretical background from stochastic and numeric analysis. A downloadable softward containing programs for over 100 problems is provided at each of the following homepages:
http://www.math.uni-frankfurt.de/~numerik/kloeden/ http://www.business.uts.edu.au/finance/staff/eckhard.html http.//www.math.siu.edu/schurz/SOFTWARE/
to enable the reader to develop an intuitive understanding of the issues involved. Applications include stochastic dynamical systems, filtering, parametric estimation and finance modeling.
The book is intended for readers without specialist stochastic background who want to apply such numerical methods to stochastic differential equations that arise in their own filed.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1994Количество страниц: 309Добавлена в каталог: 14.01.2014Операции: Положить на полку |
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Region of absolute stability 132 136 Region of attraction 223 Relative frequency 1 Richardson extrapolation 189 Risky asset 264 Romberg extrapolation 189 Roundoff error 97 106 Runge — Kutta scheme 103 240 Runge — Kutta scheme, implicit, strong order 1.0 164 Runge — Kutta scheme, implicit, strong order 1.5 165 Sample average 17 Sample mean 33 Sample path 43 Sample space 1 Sample variance 17 33 Scheme 111 Scheme, efficiency of 173 SDE, stochastic differential equation XIII Shuffling procedure 40 Simulation 112 Simulation, studies 169 201 Solution, explicit 112 Solution, pathwise unique 72 Solution, strong unique 72 Solution, weak unique 72 Stable asymptotically numerically 130 135 Standard deviation 17 Standard Gaussian distributed 13 Stiff system 133 Stochastic differential 68 Stochastic differential equation 139 Stochastic differential equation, autonomous 73 Stochastic differential equation, explicitly solv. 112 Stochastic differential equation, linear 69 74 112 158 201 264 Stochastic differential equation, matrix 74 Stochastic differential equation, nonlinear 175 Stochastic differential equation, stiff 134 Stochastic differential equation, Stratonovich 75 Stochastic differential equation, vector 73 Stochastic flow, gradient 225 Stochastic flow, on a circle 225 Stochastic flow, on a torus 227 Stochastic process, continuous time 43 Stochastic process, discrete time 43 Stratonovich integral 67 Stratonovich integral, multiple 89 148 242 Stratonovich integral, multiple, approximate 82 85 Stratonovich integral, multiple, stochastic 81 Stratonovich SDE 75 Stratonovich — Taylor expansion 80f. Strong convergence 27 Strong convergence, order 122 Student t-distribution 33 118 125 sup, supremum 10 T, often terminal time 73 t-test 33 Taylor formula 77 Taylor method truncated 101 Taylor scheme 203 Taylor scheme, 1.5 strong 146 147 Taylor scheme, 2.0 strong 148 Taylor scheme, 2.0 weak 181 203 Taylor scheme, 2.0 weak simplified 182 Taylor scheme, 3.0 weak simplified 183 204 Taylor scheme, 4.0 weak simplified 184 205 Taylor scheme, bilinear 2.0 171 Taylor scheme, implicit 1.5 strong 162 Taylor scheme, implicit 2.0 strong 163 Taylor scheme, implicit 2.0 weak 197 Taylor scheme, weak 179 Telegraphic noise process 244 Test for independence 40 Test function 27 Time approximation discrete 91 111 Time discretization 91 110 Trajectory 43 Transition matrix 43 Transition probability 44 Trapezoidal method 98 Trapezoidal method, modified 98 Two-step scheme, implicit strong order 1.0 167 Two-step scheme, implicit strong order 1.5 167 Two-step scheme, implicit strong order 2.0 168 Two-step scheme, strong order 1.0 155 Two-step scheme, strong order 1.5 156 U(a,b), uniformly distributed on [a,b] 4 Uniformly distributed 4 17 Var(X), variance of X 17 Variance 17 22 26 55 Variance reducing approximations 207 Variance reducing estimators 209 Variance reduction method 207 251 Variance reduction technique 251 Vector version Ito formula 73 Visualization 219 Volatility 265 W(t), 50 w.p.1, with probability one 2 27 Waiting time 48 Weak convergence 27 Weak convergence, order 128 Weak Taylor approximation order 1.0 179 Weak Taylor scheme 180 Weak Taylor scheme, order 2.0 181 Weak Taylor scheme, order 2.0 implicit 195 Weak Taylor scheme, order 2.0 simplified 182 Weak Taylor scheme, order 3.0 simplified 183 Weak Taylor scheme, order 4.0 simplified 184 Wiener process 50 55 56 64 Wiener process, m-dimensional 73 81 Wiener process, standard 50 Wiener process, tied-down 59 With probability one (w.p.1) 2 Zakai equation 239 [a,b], closed interval from a to b 4
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