© 2000

Random Evolutions and their Applications

New Trends


Part of the Mathematics and Its Applications book series (MAIA, volume 504)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Anatoly Swishchuk
    Pages 1-20
  3. Anatoly Swishchuk
    Pages 21-62
  4. Anatoly Swishchuk
    Pages 63-84
  5. Anatoly Swishchuk
    Pages 119-126
  6. Anatoly Swishchuk
    Pages 127-155
  7. Anatoly Swishchuk
    Pages 180-187
  8. Anatoly Swishchuk
    Pages 280-284
  9. Back Matter
    Pages 285-294

About this book


The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S)­ market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.


Martingale Stochastic model Stochastic models Stochastic processes operator statistics stochastic process

Authors and affiliations

  1. 1.Institute of MathematicsNational Academy of SciencesKievUkraine

Bibliographic information

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