Stochastic versus deterministic systems of differential equations

✍ Scribed by G. S. Ladde, M. Sambandham

• Publisher: Marcel Dekker
• Year: 2004
• Tongue: English
• Leaves: 321
• Series: Monographs and textbooks in pure and applied mathematics 260
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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