Stochastic Integration with Jumps Book

	Preface
Ch. 1	Introduction	1
1.1	Motivation: Stochastic Differential Equations	1
1.2	Wiener Process	9
1.3	The General Model	20
Ch. 2	Integrators and Martingales	43
2.1	The Elementary Stochastic Integral	46
2.2	The Semivariations	53
2.3	Path Regularity of Integrators	58
2.4	Processes of Finite Variation	67
2.5	Martingales	71
Ch. 3	Extension of the Integral	87
3.1	The Daniell Mean	88
3.2	The Integration Theory of a Mean	94
3.3	Countable Additivity in p-Mean	106
3.4	Measurability	110
3.5	Predictable and Previsible Processes	115
3.6	Special Properties of Daniell's Mean	123
3.7	The Indefinite Integral	130
3.8	Functions of Integrators	145
3.9	Ito's Formula	157
3.10	Random Measures	171
Ch. 4	Control of Integral and Integrator	187
4.1	Change of Measure - Factorization	187
4.2	Martingale Inequalities	209
4.3	The Doob-Meyer Decomposition	221
4.4	Semimartingales	232
4.5	Previsible Control of Integrators	238
4.6	Levy Processes	253
Ch. 5	Stochastic Differential Equations	271
5.1	Introduction	271
5.2	Existence and Uniqueness of the Solution	282
5.3	Stability: Differentiability in Parameters	298
5.4	Pathwise Computation of the Solution	310
5.5	Weak Solutions	330
5.6	Stochastic Flows	343
5.7	Semigroups, Markov Processes, and PDE	351
App. A	Complements to Topology and Measure Theory	363
	App. B: Answers to Selected Problems	470
	References	477
	Index of Notations	483
	Index	489