内容介绍

《带跳的随机微分方程理论及其应用(影印版)》，本书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。

编辑推荐

《带跳的随机微分方程理论及其应用(英文版)》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。

目录

preface acknowledgement abbreviations and some explanations Ⅰ stochastic differential equations 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 spacesL0 and L2 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—dimensional 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 equations 3.1 strong solutions to sde with jumps 3.1.1 notation 3.1.2 a priori estimate and uniqueness of solutions 3.1.3 existence of solutions for the lipschitzian case 3.2 exponential solutions to linear sde with jumps 3.3 girsanov transformation and weak solutions of sde with jumps 3.4 examples of weak solutions 4 some useful tools in stochastic differential equations 4.1 yamada—watanabe type theorem 4.2 tanaka type formula and some applications 4.2.1 localization technique 4.2.2 tanaka type formula in d—dimensional space 4.2.3 applications to pathwise uniqueness and convergence of solutions 4.2.4 tanaka type formual in 1—dimensional space 4.2.5 tanaka type formula in the component form 4.2.6 pathwise uniqueness of solutions 4.3 local time and occupation density formula 4.4 krylov estimation 4.4.1 the case for 1—dimensional space 4.4.2 the case for d—dimensional space 4.4.3 applications to convergence of solutions to sde with jumps 5 stochastic differential equations with non—lipschitzian co efficients 5.1 strong solutions.continuous coefficients with p—conditions 1 5.2 the skorohod weak convergence technique 5.3 weak solutions.continuous coefficients 5.4 existence of strong solutions and applications to ode 5.5 weak solutions.measurable coefficient case Ⅱ applications 6 how to use the stochastic calculus to solve sde 6.1 the foundation of applications： ito's formula and girsanov's theorem 6.2 more useful examples 7 linear and non—linear filtering 7.1 solutions of sde with functional coefficients and girsanov 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—dimensional 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 solutions 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 solutions 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 solutions for non—lipschitzian case 8.9 convergence of solutions 8.10 explanation of solutions of bsdes to financial markets 8.11 comparison theorem for bsde with jumps 8.12 explanation of comparison theorem.arbitrage—free market 8.13 solutions 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 consumption by h—j—b equation and lagrange method 9.1 optimal consumption 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 applications 9.2.5 concluding remarks 10 comparison theorem and stochastic pathwise control ' 10.1 comparison for solutions of stochastic differential equations 10.1.11—dimensional space case 10.1.2 component comparison in d—dimensional space 10.1.3 applications to existence of strong solutions.weaker conditions 10.2 weak and pathwise uniqueness for 1—dimensional sde with jumps 10.3 strong solutions for 1—dimensional 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—dimensional 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 solutions 11.4 moment estimates and uniqueness of solutions to rsde 11.5 solutions for rsde with jumps and with continuous coef—ficients 11.6 solutions for rsde with jumps and with discontinuous co—etticients 11.7 solutions to population sde and their properties 11.8 comparison of solutions and stochastic population control 11.9 caculation of solutions to population rsde 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 vectors 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 integrals references index