随机分析应用导论
2004-4
世界图书出版公司
Fima C Klebaner
321
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During the past twenty years, there has been an increasing demand for tools and methods of Stochastic Calculus in various disciplines. One of the greatest demands appears to have come from the growing area of Mathematical Finance where Stochastic Calculus is used for pricing and hedging of financial derivatives, such as options. In Engineering, most popular applications of Stochastic Calculus are in filtering and control theory. In Physics, Stochastic Calculus is used to study the effects of random excitations on various physical phenomena. In Biology, Stochastic Calculus is used to model the effects Of stochastic variability in reproduction and environment on populations.
1 Preliminaries From Calculus 1.1 Continuous and Differentiable Functions 1.2 Right and Left-Continuous Functions 1.3 Variation of a Function 1.4 Riemann Integral 1.5 Stieltjes Integral 1.6 Differentials and Integrals 1.7 Taylor‘s Formula and other results 2 Concepts of Probability Theory 2.1 Discrete Probability Model 2.2 Continuous Probability Model 2.3 Expectation and Lebesgue Integral 2.4 Transforms and Convergence 2.5 Independence and Conditioning 2.6 Stochastic Processes in Continuous Time 3 Basic Stochastic Processes 3.1 Brownian Motion 3.2 Brownian Motion as a Gaussian Process 3.3 Properties of Brownian Motion Paths 3.4 Three Martingales of Brownian Motion 3.5 Markov Property of Brownian Motion 3.6 Exit Times and Hitting Times 3.7 Maximun and Minimun of Brownian Motion 3.8 Distribution of Hitting Times 3.9 Reflection Proncipled and Joint Distrbutions 3.10 Zeros of Browinian Motion.Arcsine Law 3.11 Size of Increments of Brownian MoTion 3.12 Brownian Motion in Hight Dimensions ……4 Borwnian Motion Claculus5 Stochastic Differential Equations6 Diffusion Processes7 Martinglases8 Calculus for Semimartingales9 Pure Jump Processes10 Change of Probability Measure11 Applications in Finace12 Applications in Biology13 Applications on Engineering and PhysicsReferences
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