Stochastic versus Deterministic Systems of Differential Equations (Chapman & Hall/CRC Pure and Applied Mathematics)

Text addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and deterministic and stochastic parameter uncertainties. A text for graduate students or a reference for experimental and applied scientists. Contents ......Page 7 1.1. UPPER BOUND FOR MEAN DEVIATION......Page 15 1.2. ERROR ESTIMATES......Page 18 1.3. EIGENVALUES OF RANDOM MATRICES......Page 24 1.4. STABILITY OF RANDOM MATRICES......Page 35 1.5. APPLICATIONS......Page 38 a) Economic Analysis of Capital and Investment......Page 39 b) Free Damped Motion of Spring......Page 40 1.6. NUMERICAL EXAMPLES......Page 41 1.7. NOTES AND COMMENTS......Page 49 2.0 INTRODUCTION......Page 50 2.1. VARIATION OF CONSTANTS METHOD......Page 51 2.2. COMPARISON METHOD......Page 58 2.3. PROBABILITY DISTRIBUTION METHOD......Page 71 2.4. STABILITY ANALYSIS......Page 79 2.5. ERROR ESTIMATES......Page 96 2.6. RELATIVE STABILITY......Page 113 2.7. APPLICATIONS TO POPULATION DYNAMICS......Page 123 2.8. NUMERICAL EXAMPLES......Page 135 2.9 NOTES AND COMMENTS......Page 142 3.0 INTRODUCTION......Page 144 3.1. GREEN'S FUNCTION METHOD......Page 145 3.2. COMPARISON METHOD......Page 152 3.3. PROBABILITY DISTRIBUTION METHOD......Page 163 3.4. SOLVABILITY AND UNIQUENESS ANALYSIS......Page 178 3.5. STABILITY ANALYSIS......Page 182 3.6. ERROR ESTIMATES......Page 187 3.7. RELATIVE STABILITY......Page 193 a) SLIDER AND RIGID ROLLER BEARING PROBLEMS......Page 197 b) THE HANGING CABLE PROBLEM......Page 221 3.9. NUMERICAL EXAMPLES......Page 226 3.10 NOTES AND COMMENTS......Page 230 4.0. INTRODUCTION......Page 231 4.1. VARIATION OF CONSTANTS METHOD......Page 232 4.2. COMPARISON METHOD......Page 239 4.3. PROBABILITY DISTRIBUTION METHOD......Page 246 4.4. STABILITY ANALYSIS......Page 250 4.5. ERROR ESTIMATES......Page 257 4.6. RELATIVE STABILITY......Page 264 4.7. APPLICATIONS TO POPULATION DYNAMICS......Page 267 4.8. NUMERICAL EXAMPLES......Page 274 4.9. NOTES AND COMMENTS......Page 278 5.1. GREEN'S FUNCTION METHOD......Page 279 5.2. STABILITY ANALYSIS......Page 289 5.3. ERROR ESTIMATES......Page 292 5.4. RELATIVE STABILITY......Page 297 5.5. NOTES AND COMMENTS......Page 299 A.1. CONVERGENCE OF RANDOM SEQUENCES......Page 300 A.2. INITIAL VALUE PROBLEMS......Page 302 A.3. BOUNDARY VALUE PROBLEMS......Page 309 REFERENCES......Page 311

This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic.

An estimate on the variation of a random function with the corresponding smooth function is presented in Section 1.1.