Applied Stochastic Processes and Con
Jump-Di usions: Modeling, Analys
Computation
FloydB. Hanson
University ofIllinois
Chicago,Illinois,USA
John J. Westman
MiamiUniversity
Oxford, Ohio,USA
April19,2003

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ii Contents
2.4 StochasticChainRuleforJump-Di usions . . . . . . . . . . . . 38
2.5 MoreAboutThisChapter . . . . . . . . . . . . . . . . . . . . . 40
2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 SDEswithSpace-TimeandState-DependentPoissonNoise 43
3.1 Space-TimePoissonProcess . . . . . . . . . . . . . . . . . . . . 43
3.2 State-DependentGeneralizationofPoissonProcesses . . . . . . 45
3.3 State-DependentSDEs . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 MoreAboutThisChapter . . . . . . . . . . . . . . . . . . . . . 47
4 Stochastic CalculusforGeneral Markov SDEs 49
4.1 Multi-DimensionalMarkovSDE . . . . . . . . . . . . . . . . . . 49
4.2 StochasticChainRuleinMulti-Dimensions. . . . . . . . . . . . 50
4.3 ConditionalIn nitesimalMomentsinMulti-Dimensions. . . . . 51
4.4 MoreAboutThisChapter . . . . . . . . . . . . . . . . . . . . . 51
4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 DeterministicOptimalControl 53
5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6 Stochastic DynamicProgramming 55
6.1 StochasticOptimalControlProblem . . . . . . . . . . . . . . . 55
6.2 Bellman'sPrincipleofOptimality . . . . . . . . . . . . . . . . . 56
6.3 HJBEquationofStochasticDynamicProgramming . . . . . . . 57
6.4 MoreAboutThisChapter . . . . . . . . . . . . . . . . . . . . . 59
6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 KolmogorovForward Equation 61
7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
8 ComputationalMethodsforSDP 63
9 ApplicationsinFinancialEngineering 65
10 ApplicationsinMathematicalBiology 67
11 ApplicationsinStochastic Manufacturing Systems 69
12 AppliedGuidetoAbstract Stochastic Processes 71
Bibliography 73

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