What is included with this book?
1. Introduction | 1 | (6) | |||
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1 | (1) | |||
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2 | (1) | |||
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2 | (1) | |||
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3 | (1) | |||
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4 | (1) | |||
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4 | (3) | |||
2. Some Mathematical Preliminaries | 7 | (14) | |||
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7 | (4) | |||
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11 | (4) | |||
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15 | (6) | |||
3. Itô Integrals | 21 | (22) | |||
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21 | (9) | |||
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30 | (4) | |||
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34 | (3) | |||
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37 | (6) | |||
4. The Itô Formula and the Martingale Representation Theorem | 43 | (20) | |||
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43 | (5) | |||
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48 | (1) | |||
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49 | (5) | |||
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54 | (9) | |||
5. Stochastic Differential Equations | 63 | (20) | |||
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63 | (5) | |||
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68 | (4) | |||
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72 | (2) | |||
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74 | (9) | |||
6. The Filtering Problem | 83 | (30) | |||
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83 | (2) | |||
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85 | (19) | |||
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104 | (1) | |||
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105 | (8) | |||
7. Diffusions: Basic Properties | 113 | (26) | |||
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113 | (3) | |||
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116 | (5) | |||
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121 | (3) | |||
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124 | (2) | |||
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126 | (2) | |||
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128 | (11) | |||
8. Other Topics in Diffusion Theory | 139 | (36) | |||
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139 | (4) | |||
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143 | (3) | |||
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146 | (2) | |||
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148 | (5) | |||
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153 | (6) | |||
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159 | (9) | |||
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168 | (7) | |||
9. Applications to Boundary Value Problems | 175 | (30) | |||
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175 | (3) | |||
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178 | (12) | |||
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190 | (7) | |||
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197 | (8) | |||
10. Application to Optimal Stopping | 205 | (30) | |||
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205 | (12) | |||
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217 | (5) | |||
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222 | (2) | |||
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224 | (4) | |||
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228 | (7) | |||
11. Application to Stochastic Control | 235 | (26) | |||
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235 | (2) | |||
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237 | (14) | |||
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251 | (1) | |||
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252 | (9) | |||
12. Application to Mathematical Finance | 261 | (44) | |||
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261 | (10) | |||
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271 | (8) | |||
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279 | (19) | |||
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298 | (7) | |||
Appendix A: Normal Random Variables | 305 | (4) | |||
Appendix B: Conditional Expectation | 309 | (2) | |||
Appendix C: Uniform Integrability and Martingale Convergence | 311 | (4) | |||
Appendix D: An Approximation Result | 315 | (4) | |||
Solutions and Additional Hints to Some of the Exercises | 319 | (26) | |||
References | 345 | (8) | |||
List of Frequently Used Notation and Symbols | 353 | (4) | |||
Index | 357 |
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