Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

ISBN: 978-0-387-87861-4 (Print) 978-0-387-87862-1 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-x

  2. No Access

    Book Chapter

    Pages 1-10

    Definition of stochastic process. Cylinder σ-algebra, finite-dimensional distributions, the Kolmogorov theorem

  3. No Access

    Book Chapter

    Pages 11-19

    Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions

  4. No Access

    Book Chapter

    Pages 21-32

    Trajectories. Modifications. Filtrations

  5. No Access

    Book Chapter

    Pages 33-42

    Continuity. Differentiability. Integrability

  6. No Access

    Book Chapter

    Pages 43-58

    Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures

  7. No Access

    Book Chapter

    Pages 59-70

    Gaussian processes

  8. No Access

    Book Chapter

    Pages 71-105

    Martingales and related processes in discrete and continuous time. Stopping times

  9. No Access

    Book Chapter

    Pages 107-127

    Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values

  10. No Access

    Book Chapter

    Pages 129-136

    Prediction and interpolation

  11. No Access

    Book Chapter

    Pages 137-158

    Markov chains: Discrete and continuous time

  12. No Access

    Book Chapter

    Pages 159-173

    Renewal theory. Queueing theory

  13. No Access

    Book Chapter

    Pages 175-192

    Markov and diffusion processes

  14. No Access

    Book Chapter

    Pages 193-213

    Itô stochastic integral. Itô formula. Tanaka formula

  15. No Access

    Book Chapter

    Pages 215-228

    Stochastic differential equations

  16. No Access

    Book Chapter

    Pages 229-240

    Optimal stopping of random sequences and processes

  17. No Access

    Book Chapter

    Pages 241-270

    Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems

  18. No Access

    Book Chapter

    Pages 271-302

    Statistics of stochastic processes

  19. No Access

    Book Chapter

    Pages 303-313

    Stochastic processes in financial mathematics (discrete time)

  20. No Access

    Book Chapter

    Pages 315-326

    Stochastic processes in financial mathematics (continuous time)

  21. No Access

    Book Chapter

    Pages 327-357

    Basic functionals of the risk theory

  22. Back Matter

    Pages 1-17