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Applied Probability From Random Sequences to Stochastic Processes [Hardcover]

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  • Category: Books (Mathematics)
  • Author:  Girardin, Val?rie, Limnios, Nikolaos
  • Author:  Girardin, Val?rie, Limnios, Nikolaos
  • ISBN-10:  3319974114
  • ISBN-10:  3319974114
  • ISBN-13:  9783319974118
  • ISBN-13:  9783319974118
  • Publisher:  Springer
  • Publisher:  Springer
  • Binding:  Hardcover
  • Binding:  Hardcover
  • Pub Date:  01-Apr-2018
  • Pub Date:  01-Apr-2018
  • SKU:  3319974114-11-SPRI
  • SKU:  3319974114-11-SPRI
  • Item ID: 101538962
  • List Price: $84.99
  • Seller: ShopSpell
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  • Delivery by: Jan 31 to Feb 02
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This textbook addresses postgraduate students in applied mathematics, probability, and statistics, as well as computer scientists, biologists, physicists and economists, who are seeking a rigorous introduction to applied stochastic processes. Pursuing a pedagogic approach, the content follows a path of increasing complexity, from the simplest random sequences to the advanced stochastic processes. Illustrations are provided from many applied fields, together with connections to ergodic theory, information theory, reliability and insurance. The main content is also complemented by a wealth of examples and exercises with solutions.



Notation iii
Preface ix
1 Independent Random Sequences 1
1.1 Denumerable Sequences . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Sequences of Events . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Independence . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Analytic Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.1 Generating Functions . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Characteristic Functions . . . . . . . . . . . . . . . . . . . 13
1.2.3 Laplace Transforms . . . . . . . . . . . . . . . . . . . . . 15
1.2.4 Moment Generating Functions and Cram?er Transforms . 17
1.2.5 From Entropy to Entropy Rate . . . . . . . . . . . . . . . 19
1.3 Sums and Random Sums . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.1 Sums of Independent Variables . . . . . . . . . . . . . . . 23
1.3.2 Random Sums . . . . . . . . . . . . . . . . . . . . . . . . 27&llÓ'