| Notations |
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ix | |
| Introduction |
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xi | |
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Chapter 1 Stationary Increments of Discrete Time Stochastic Processes: Spectral Representation |
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1 | (8) |
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Chapter 2 Extrapolation Problem for Stochastic Sequences with Stationary nth Increments |
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9 | (22) |
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2.1 The classical method of extrapolation |
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9 | (12) |
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2.2 Minimax (robust) method of extrapolation |
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21 | (3) |
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2.3 Least favorable spectral density in the class D0f |
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24 | (1) |
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2.4 Least favorable spectral densities which admit factorization in the class D0f |
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25 | (4) |
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2.5 Least favorable spectral density in the class Duu |
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29 | (1) |
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2.6 Least favorable spectral density which admits factorization in the class Duu |
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29 | (2) |
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Chapter 3 Interpolation Problem for Stochastic Sequences with Stationary nth Increments |
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31 | (22) |
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3.1 The classical method of interpolation |
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31 | (10) |
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3.2 Minimax method of interpolation |
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41 | (2) |
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3.3 Least favorable spectral densities in the class D-0,n |
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43 | (4) |
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3.4 Least favorable spectral densities in the class D-M,n |
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47 | (6) |
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Chapter 4 Extrapolation Problem for Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise |
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53 | (36) |
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4.1 The classical method of extrapolation with noise |
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53 | (18) |
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4.2 Extrapolation of cointegrated stochastic sequences |
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71 | (4) |
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4.3 Minimax (robust) method of extrapolation |
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75 | (5) |
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4.4 Least favorable spectral densities in the class D0f × D0g |
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80 | (2) |
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4.5 Least favorable spectral densities which admit factorization in the class D0f × D&0g |
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82 | (2) |
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4.6 Least favorable spectral densities in the class Duu × Dε |
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84 | (2) |
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4.7 Least favorable spectral densities which admit factorization in the class Duu × Dε |
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86 | (3) |
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Chapter 5 Interpolation Problem for Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise |
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89 | (18) |
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5.1 The classical method of interpolation with noise |
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89 | (7) |
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5.2 Interpolation of cointegrated stochastic sequences |
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96 | (1) |
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5.3 Minimax (robust) method of interpolation |
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97 | (3) |
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5.4 Least favorable spectral densities in the class D-0,f × D-0,g |
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100 | (3) |
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5.5 Least favorable spectral densities in the class D2ε1 × D1ε2 |
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103 | (4) |
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Chapter 6 Filtering Problem of Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise |
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107 | (32) |
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6.1 The classical method of filtering |
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107 | (12) |
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6.2 Filtering problem for cointegrated stochastic sequences |
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119 | (5) |
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6.3 Minimax (robust) method of filtering |
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124 | (5) |
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6.4 Least favorable spectral densities in the class D0f × D0g |
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129 | (2) |
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6.5 Least favorable spectral densities which admit factorization in the class D0f × D0g |
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131 | (3) |
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6.6 Least favorable spectral densities in the class Duu × Dε |
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134 | (1) |
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6.7 Least favorable spectral densities which admit factorization in the class Duu × Dε |
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135 | (4) |
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Chapter 7 Interpolation Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise |
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139 | (16) |
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7.1 The classical interpolation problem in the case of non-stationary noise |
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140 | (8) |
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7.2 Minimax (robust) method of interpolation |
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148 | (2) |
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7.3 Least favorable spectral densities in the class D-0,μ × D-0,μ |
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150 | (3) |
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7.4 Least favorable spectral densities in the class D-M,μ × D-M,μ |
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153 | (2) |
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Chapter 8 Filtering Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise |
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155 | (26) |
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8.1 The classical filtering problem in the case of non-stationary noise |
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156 | (14) |
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8.2 Minimax filtering based on observations with non-stationary noise |
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170 | (4) |
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8.3 Least favorable spectral densities in the class D0f × D0g |
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174 | (1) |
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8.4 Least favorable spectral densities which admit factorizations in the class D0f × D0g |
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175 | (2) |
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8.5 Least favorable spectral densities in the class Duv × Dε |
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177 | (1) |
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8.6 Least favorable spectral densities which admit factorizations in the class Duv × Dε |
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178 | (3) |
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Chapter 9 Stationary Increments of Continuous Time Stochastic Processes: Spectral Representation |
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181 | (6) |
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Chapter 10 Extrapolation Problem for Stochastic Processes with Stationary nth Increments |
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187 | (30) |
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10.1 Hilbert space projection method of extrapolation |
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187 | (18) |
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10.2 Minimax (robust) method extrapolation |
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205 | (3) |
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10.3 Least favorable spectral densities in the class D0f × D0g |
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208 | (2) |
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10.4 Least favorable spectral density in the class D0f |
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210 | (1) |
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10.5 Least favorable spectral density which admits factorization in the class D0f |
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211 | (2) |
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10.6 Least favorable spectral densities in the class Duv × Dε |
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213 | (2) |
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10.7 Least favorable spectral densities which allow factorization in the class Dδ |
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215 | (2) |
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Chapter 11 Interpolation Problem for Stochastic Processes with Stationary nth Increments |
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217 | (22) |
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11.1 Hilbert space projection method of interpolation |
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217 | (9) |
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11.2 Minimax (robust) method of interpolation |
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226 | (3) |
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11.3 Least favorable spectral densities in the class D0f × D0g |
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229 | (1) |
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11.4 Least favorable spectral density in the class D0f |
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230 | (1) |
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11.5 Least favorable spectral densities in the class D01/f × D01/g |
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231 | (2) |
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11.6 Least favorable spectral density in the class D01/f |
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233 | (1) |
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11.7 Least favorable spectral densities in the class Duv × Dε |
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234 | (1) |
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11.8 Least favorable spectral density in the class Duu |
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235 | (1) |
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11.9 Least favorable spectral density in the class D2ε |
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236 | (3) |
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Chapter 12 Filtering Problem for Stochastic Processes with Stationary nth Increments |
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239 | (14) |
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12.1 Hilbert space projection method of filtering |
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239 | (7) |
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12.2 Minimax (robust) method of filtering |
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246 | (2) |
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12.3 Least favorable spectral densities in the class D0f × D0g |
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248 | (2) |
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12.4 Least favorable spectral densities in the class Duv × Dδ |
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250 | (3) |
| Problems to Solve |
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253 | (6) |
| Appendix |
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259 | (8) |
| References |
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267 | (14) |
| Index |
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281 | |
