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List of figures | p. x |
Preface | p. xi |
Frequently used notation | p. xiii |
Introduction | p. 1 |
Probabilistic framework | p. 6 |
Introduction | p. 6 |
Basic setting | p. 6 |
Probability spaces | p. 6 |
Random variables | p. 7 |
Expectation | p. 8 |
Radon-Nikodym derivatives | p. 10 |
Conditional expectation and independence | p. 11 |
Random sequences | p. 15 |
Martingales and stopping times | p. 18 |
Martingales | p. 19 |
Stopping times | p. 24 |
Continuous-time analogs | p. 26 |
Brownian motion and Poisson processes | p. 27 |
Brownian motion | p. 28 |
Poisson processes | p. 30 |
Continuous-time semimartingales | p. 32 |
Stochastic integration | p. 34 |
Markov optimal stopping theory | p. 40 |
Introduction | p. 40 |
Markov optimal stopping problems | p. 40 |
The finite-horizon case: dynamic programming | p. 41 |
The general case | p. 41 |
The Markov case | p. 46 |
The infinite-horizon case | p. 50 |
A martingale interpretation of the finite-horizon results | p. 51 |
The infinite-horizon case for bounded reward | p. 52 |
The general infinite-horizon case | p. 55 |
The infinite-horizon case with Markov rewards | p. 59 |
Markov optimal stopping in continuous time | p. 60 |
Appendix: a proof of Lemma 3.8 | p. 61 |
Sequential detection | p. 65 |
Introduction | p. 65 |
Optimal detection | p. 65 |
Performance analysis | p. 74 |
The continuous-time case | p. 81 |
The Brownian case | p. 81 |
The Brownian case - an alternative proof | p. 86 |
An interesting extension of Wald-Wolfowitz | p. 90 |
The case of Itô processes | p. 91 |
The Poisson case | p. 93 |
The compound Poisson case | p. 100 |
Discussion | p. 101 |
Bayesian quickest detection | p. 102 |
Introduction | p. 102 |
Shiryaev's problem | p. 103 |
The continuous-time case | p. 109 |
Brownian observations | p. 109 |
Poisson observations | p. 115 |
A probability maximizing approach | p. 122 |
Other penalty functions | p. 124 |
A game theoretic formulation | p. 125 |
Discussion | p. 128 |
Non-Bayesian quickest detection | p. 130 |
Introduction | p. 130 |
Lorden's problem | p. 130 |
Performance of Page's test | p. 142 |
The continuous-time case | p. 144 |
Brownian observations | p. 144 |
It&ocaron; processes | p. 150 |
Brownian motion with an unknown drift parameter | p. 152 |
Poisson observations | p. 154 |
Asymptotic results | p. 157 |
Lorden's approach | p. 158 |
Brownian motion with two-sided alternatives | p. 167 |
Comments on the false-alarm constraint | p. 171 |
Discussion | p. 172 |
Additional topics | p. 174 |
Introduction | p. 174 |
Decentralized sequential and quickest detection | p. 175 |
Decentralized sequential detection with a fusion center | p. 176 |
Decentralized quickest detection with a fusion center | p. 184 |
Decentralized sequential detection without fusion | p. 189 |
Quickest detection with modeling uncertainty | p. 194 |
Robust quickest detection | p. 194 |
Adaptive quickest detection | p. 200 |
Quickest detection with dependent observations | p. 201 |
Quickest detection with independent likelihood ratio sequences | p. 201 |
Locally asymptotically normal distributions | p. 203 |
Sequential detection (local hypothesis approach) | p. 205 |
Quickest detection (local hypothesis approach) | p. 210 |
Bibliography | p. 213 |
Index | p. 225 |
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