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| 008 | 140801s1957 xx 000 0 und d | ||
| 020 | _a9788126518050 | ||
| 082 | _a519.2 FEL-I;Vol-I | ||
| 100 | _aFeller, William | ||
| 245 | _aIntroduction to Probability :`Theory and its Applications Vol - l | ||
| 250 | _a3rd | ||
| 260 |
_bWiley India _c1957 _aNew Delhi |
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| 300 | _a509p. | ||
| 500 | _aContents The Exponential and the Uniform Densities 1 Densities Convolutions 3 The Exponential Density 8 Waiting Time Paradoxes The Poisson Process 11 The Persistence of Bad Luck 15 Waiting Times and Order Statistics 17 The Uniform Distribution 21 Random Splittings 25 Terminating Transient Processes 374 Diverse Applications 377 Existence of Limits in Stochastic Processes 379 9 Renewal Theory on the Whole Line 380 Problems for Solution 385 Random Walks in 311 389 Basic Concepts and Notations 390 Duality Types of Random Walks 394 Convolutions and Covering Theorems 26 Random Directions 29 The Use of Lebesgue Measure 33 Empirical Distributions 36 Problems for Solution 39 Special Densities Randomization 45 Gamma Distributions 47 3 Related Distributions of Statistics 48 Some Common Densities 49 Randomization and Mixtures 53 Discrete Distributions 55 CHAPTER 66 chapter 103 CHAPTER 127 Symmetrization 148 Integration by Parts Existence of Moments 150 Chebyshevs Inequality 151 Further Inequalities Convex Functions 152 Simple Conditional Distributions Mixtures 156 Starred sections are not required for the understanding of the sequel and should be omitted at first readme 160 11 Conditional Expectations 162 Problems for Solution 165 A Survey of some Important Distributions and Processes 169 Examples 173 Infinitely Divisible Distributions in Rl 176 Processes with Independent Increments 179 5 Ruin Problems in Compound Poisson Processes 182 Renewal Processes 184 Examples and Problems 187 Random Walks 190 The Queuing Process 194 Persistent and Transient Random Walks 200 General Markov Chains 205 12 Martingales 209 Problems for Solution 215 Laws of Large Numbers Applications in Analysis 219 Bernstein Polynomials Absolutely Monotone Functions 222 Moment Problems 224 4 Application to Exchangeable Variables 228 5 Generalized Taylor Formula and SemiGroups 230 Inversion Formulas for Laplace Transforms 232 7 Laws of Large Numbers for Identically Distributed Variables 234 8 Strong Laws 237 9 Generalization to Martingales 241 Problems for Solution 244 The Basic Limit Theorems 247 Special Properties 252 Distributions as Operators 254 The Central Limit Theorem 258 5 Infinite Convolutions 265 Selection Theorems 267 7 Ergodic Theorems for Markov Chains 270 Regular Variation 275 9 Asymptotic Properties of Regularly Varying Functions 279 Problems for Solution 284 chapter K Infinitely Divisible Distributions and SemiGroups 290 Convolution SemiGroups 293 Preparatory Lemmas 296 Finite Variances 298 The Main Theorems 300 Stable SemiGroups 305 Triangular Arrays with Identical Distributions 308 Domains of Attraction 312 Variable Distributions The ThreeSeries Theorem 316 Problems for Solution 318 Markov Processes and SemiGroups 321 The PseudoPoisson Type 322 Linear Increments 324 Jump Processes 326 Diffusion Processes in 311 332 The Forward Equation Boundary Conditions 337 Diffusion in Higher Dimensions 344 Subordinated Processes 345 Markov Processes and SemiGroups 349 The Exponential Formula of SemiGroup Theory 353 Generators The Backward Equation 356 Renewal Theory 358 Proof of the Renewal Theorem 364 3 Refinements 366 Persistent Renewal Processes 368 The Number Nt of Renewal Epochs 372 Distribution of Ladder Heights WienerHopf Factor ization 398 3a The WienerHopf Integral Equation 402 Examples 404 Applications 408 A Combinatorial Lemma 412 Distribution of Ladder Epochs 413 The Arc Sine Laws 417 Miscellaneous Complements 423 Problems for Solution 425 Laplace Transforms Tauberian Theorems Resolvents 429 Elementary Properties 434 Examples 436 Completely Monotone Functions Inversion Formulas 439 Tauberian Theorems 442 6 Stable Distributions 448 7 Infinitely Divisible Distributions 449 8 Higher Dimensions 452 Laplace Transforms for SemiGroups 454 The HilleYosida Theorem 459 Problems for Solution 463 Applications of Laplace Transforms 466 Examples 468 Limit Theorems Involving Arc Sine Distributions 470 Busy Periods and Related Branching Processes 473 Diffusion Processes 475 BirthandDeath Processes and Random Walks 479 The Kolmogorov Differential Equations 483 The Pure Birth Process 488 Calculation of Ergodic Limits and of FirstPassage Times 491 Problems for Solution 495 Characteristic Functions 498 Special Distributions Mixtures 502 2a Some Unexpected Phenomena 505 Uniqueness Inversion Formulas 507 Regularity Properties 511 The Central Limit Theorem for Equal Components 515 The Lindeberg Conditions 518 Characteristic Functions in Higher Dimensions 521 8 Two Characterizations of the Normal Distribution 525 Problems for Solution 526 CHAPTER XVI Expansions Related to the Central Limit Theorem 531 Notations 532 Expansions for Densities 533 Smoothing 536 Expansions for Distributions 538 The BerryEsseen Theorems 543 Expansions in the Case of Varying Components 546 Large Deviations 549 Infinitely Divisible Distributions 554 Canonical Forms The Main Limit Theorem 558 2a Derivatives of Characteristic Functions 565 Examples and Special Properties 566 Special Properties 570 Stable Distributions and Their Domains of Attraction 574 6 Stable Densities 581 Triangular Arrays 583 8 The Class L 588 9 Partial Attraction Universal Laws 590 10 Infinite Convolutions 592 Higher Dimensions 593 Problems for Solution 595 Applications of Fourier Methods to Random Walks 598 2 Finite Intervals Walds Approximation 601 The WienerHopf Factorization 604 Implications and Applications 609 Two Deeper Theorems 612 Criteria for Persistency 614 Problems for Solution 616 Harmonic Analysis 619 Positive Definite Functions 620 Stationary Processes 623 Fourier Series 626 5 The Poisson Summation Formula 629 Positive Definite Sequences 633 L2 Theory 635 Stochastic Processes and Integrals 641 Problems for Solution 647 Answers to Problems 651 Some Books on Cognate Subjects 655 Index 657 Copyright | ||
| 856 | _uhttps://books.google.co.in/books?id=OXkg-LvRgjUC&printsec=frontcover&dq=an+introduction+to+probability+theory+and+its+applications&hl=en&sa=X&ved=0ahUKEwiK_KC_z5bnAhVWzTgGHa8lBEYQ6AEILzAB#v=onepage&q=an%20introduction%20to%20probability%20theory%20and%20its%20applications&f=false | ||
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