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带跳的随机微分方程理论及应用 版权信息
- ISBN:9787510040566
- 条形码:9787510040566 ; 978-7-5100-4056-6
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 所属分类:>>
带跳的随机微分方程理论及应用 内容简介
司徒荣编著的《带跳的随机微分方程理论及其应用(英文影印版)》是一部讲述随机微分方程及其应用的教程。内容全面,讲述如何很好地引入和理解ito积分,确定了ito微分规则,解决了求解sde的方法,阐述了girsanov定理,并且获得了sde的弱解。书中也讲述了如何解决滤波问题、鞅表示定理,解决了金融市场的期权定价问题以及著名的black-scholes公式和其他重要结果。特别地,书中提供了研究市场中金融问题的倒向随机技巧和反射sed技巧,以便更好地研究优化随机样本控制问题。这两个技巧十分高效有力,还可以应用于解决自然和科学中的其他问题。
带跳的随机微分方程理论及应用 目录
prefaceacknowledgementabbreviatio and some explanatioⅠ stochastic differential equatio with jumps inrd 1 martingale theory and the stochastic integral for point processes 1.1 concept of a martingale 1.2 stopping times. predictable process 1.3 martingales with discrete time 1.4 uniform integrability and martingales 1.5 martingales with continuous time 1.6 doob-meyer decomposition theorem 1.7 poisson random measure and its existence 1.8 poisson point process and its existence 1.9 stochastic integral for point process. square integrable mar tingales 2 brownian motion, stochastic integral and ito's formula 2.1 brownian motion and its nowhere differentiability 2.2 spaces ~0 and z? 2.3 ito's integrals on l2 2.4 ito's integrals on l2,loc 2.5 stochastic integrals with respect to martingales 2.6 ito's formula for continuous semi-martingales 2.7 ito's formula for semi-martingales with jumps 2.8 ito's formula for d-dimeional semi-martingales. integra tion by parts 2.9 independence of bm and poisson point processes 2.10 some examples 2.11 strong markov property of bm and poisson point processes 2.12 martingale representation theorem 3 stochastic differential equatio 3.1 strong solutio to sde with jumps 3.1.1 notation 3.1.2 a priori estimate and uniqueness of solutio 3.1.3 existence of solutio for the lipschitzian case 3.2 exponential solutio to linear sde with jumps 3.3 gianov traformation and weak solutio of sde with jumps 3.4 examples of weak solutio 4 some useful tools in stochastic differential equatio 4.1 yamada-watanabe type theorem 4.2 tanaka type formula and some applicatio 4.2.1 localization technique 4.2.2 tanaka type formula in d-dimeional space 4.2.3 applicatio to pathwise uniqueness and convergence of solutio 4.2.4 tanaka type formual in 1-dimeional space 4.2.5 tanaka type formula in the component form 4.2.6 pathwise uniqueness of solutio 4.3 local time and occupation deity formula 4.4 krylov estimation 4.4.1 the case for 1-dimeional space 4.4.2 the case for d-dimeional space 4.4.3 applicatio to convergence of solutio to sde with jumps 5 stochastic differential equatio with non-lipschitzian co efficients 5.1 strong solutio. continuous coefficients with p- conditio 1 5.2 the skorohod weak convergence technique 5.3 weak solutio. continuous coefficients 5.4 existence of strong solutio and applicatio to ode 5.5 weak solutio. measurable coefficient caseⅡ applicatio 6 how to use the stochastic calculus to solve sde 6.1 the foundation of applicatio: ito's formula and gianov's theorem 6.2 more useful examples 7 linear and non-linear filtering 7.1 solutio of sde with functional coefficients and gianov theorems 7.2 martingale representation theorems (functional coefficient case) 7.3 non-linear filtering equation 7.4 optimal linear filtering 7.5 continuous linear filtering. kalman-bucy equation 7.6 kalman-bucy equation in multi-dimeional case 7.7 more general continuous linear filtering 7.8 zakai equation 7.9 examples on linear filtering 8 option pricing in a financial market and bsde 8.1 introduction 8.2 a more detailed derivation of the bsde for option pricing 8.3 existence of solutio with bounded stopping times 8.3.1 the general model and its explanation 8.3.2 a priori estimate and uniqueness of a solution 8.3.3 existence of solutio for the lipschitzian case 8.4 explanation of the solution of bsde to option pricing 8.4.1 continuous case 8.4.2 discontinuous case 8.5 black-scholes formula for option pricing. two approaches 8.6 black-scholes formula for markets with jumps 8.7 more general wealth processes and bsdes 8.8 existence of solutio for non-lipschitzian case 8.9 convergence of solutio 8.10 explanation of solutio of bsdes to financial markets 8.11 comparison theorem for bsde with jumps 8.12 explanation of comparison theorem. arbitrage-free market 8.13 solutio for unbounded (terminal) stopping times 8.14 minimal solution for bsde with discontinuous drift 8.15 existence of non-lipschitzian optimal control. bsde case 8.16 existence of discontinuous optimal control. bsdes in rl 8.17 application to pde. feynman-kac formula 9 optimal coumption by h-j-b equation and lagrange method 9.1 optimal coumption 9.2 optimization for a financial market with jumps by the lagrange method 9.2.1 introduction 9.2.2 models 9.2.3 main theorem and proof 9.2.4 applicatio 9.2.5 concluding remarks 10 comparison theorem and stochastic pathwise control ' 10.1 comparison for solutio of stochastic differential equatio 10.1.1 1-dimeional space case 10.1.2 component comparison in d-dimeional space 10.1.3 applicatio to existence of strong solutio. weaker conditio 10.2 weak and pathwise uniqueness for 1-dimeional sde with jumps 10.3 strong solutio for 1-dimeional sde with jumps 10.3.1 non-degenerate case 10.3.2 degenerate and partially-degenerate case 10.4 stochastic pathwise bang-bang control for a non-linear system 10.4.1 non-degenerate case 10.4.2 partially-degenerate case 10.5 bang-bang control for d-dimeional non-linear systems 10.5.1 non-degenerate case 10.5.2 partially-degenerate case 11 stochastic population conttrol and reflecting sde 11.1 introduction 11.2 notation 11.3 skorohod's problem and its solutio 11.4 moment estimates and uniqueness of solutio to de 11.5 solutio for de with jumps and with continuous coef- ficients 11.6 solutio for de with jumps and with discontinuous co- etticients 11.7 solutio to population sde and their properties 11.8 comparison of solutio and stochastic population control 11.9 caculation of solutio to population de 12 maximum principle for stochastic systems with jumps 12.1 introduction 12.2 basic assumption and notation 12.3 maximum principle and adjoint equation as bsde with jumps 12.4 a simple example 12.5 intuitive thinking on the maximum principle 12.6 some lemmas 12.7 proof of theorem 354 a a short review on basic probability theory a.1 probability space, random variable and mathematical ex- pectation a.2 gaussian vecto and poisson random variables a.3 conditional mathematical expectation and its properties a.4 random processes and the kolmogorov theorem b space d and skorohod's metric c monotone class theorems. convergence of random processes41 c.1 monotone class theorems c.2 convergence of random variables c.3 convergence of random processes and stochastic integralsreferencesindex
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