Stochastic Processes
eBook - PDF

Stochastic Processes

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Stochastic Processes

About this book

This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

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Yes, you can access Stochastic Processes by Richard F. Bass in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Frequently used notation
  8. 1 Basic notions
  9. 2 Brownian motion
  10. 3 Martingales
  11. 4 Markov properties of Brownian motion
  12. 5 The Poisson process
  13. 6 Construction of Brownian motion
  14. 7 Path properties of Brownian motion
  15. 8 The continuity of paths
  16. 9 Continuous semimartingales
  17. 10 Stochastic integrals
  18. 11 Ito's formula
  19. 12 Some applications of Ito's formula
  20. 13 The Girsanov theorem
  21. 14 Local times
  22. 15 Skorokhod embedding
  23. 16 The general theory of processes
  24. 17 Processes with jumps
  25. 18 Poisson point processes
  26. 19 Framework for Markov processes
  27. 20 Markov properties
  28. 21 Applications of the Markov properties
  29. 22 Transformations of Markov processes
  30. 23 Optimal stopping
  31. 24 Stochastic differential equations
  32. 25 Weak solutions of SDEs
  33. 26 The Ray–Knight theorems
  34. 27 Brownian excursions
  35. 28 Financial mathematics
  36. 29 Filtering
  37. 30 Convergence of probability measures
  38. 31 Skorokhod representation
  39. 32 The space C[0,1]
  40. 33 Gaussian processes
  41. 34 The space D[0,1]
  42. 35 Applications of weak convergence
  43. 36 Semigroups
  44. 37 Infinitesimal generators
  45. 38 Dirichlet forms
  46. 39 Markov processes and SDEs
  47. 40 Solving partial differential equations
  48. 41 One-dimensional diffusions
  49. 42 Levy processes
  50. Appendix A Basic probability
  51. Appendix B Some results from analysis
  52. Appendix C Regular conditional probabilities
  53. Appendix D Kolmogorov extension theorem
  54. References
  55. Index