This research monograph concerns the design and analysis of discrete-time
approximations for stochastic differential equations (SDEs) driven by Wiener
processes and Poisson processes or Poisson jump measures. In financial and
actuarial modeling and other areas of application, such jump diffusions are
often used to describe the dynamics of various state variables. In finance these
may represent, for instance, asset prices, credit ratings, stock indices, interest
rates, exchange rates or commodity prices.
We have attempted to explain the concepts which have been used and
developed to model the stochastic dynamics of natural and biological systems.
While the theory of stochastic differential equations and stochastic processes
provide an attractive framework with an intuitive appeal to many problems
with naturally induced variations, the solutions to such models are an active
area of research, which is in its infancy. Therefore, this book should provide
a large number of areas to research further.
Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief,
in constructing and exploiting natural differentiable structures on abstract
probability spaces; in other words, Stochastic Calculus of Variations proceeds
from a merging of differential calculus and probability theory.
As optimization under a random environment is at the heart of mathematical
finance, and as differential calculus is of paramount importance for the
search of extrema, it is not surprising that Stochastic Calculus of Variations
appears in mathematical finance.
This book represents recent research on tropical cyclones and their impact, and a wide range of topics are covered. An updated global climatology is presented, including the global occurrence of tropical cyclones and the terrestrial factors that may contribute to the variability and long-term trends in their occurrence. Research also examines long term trends in tropical cyclone occurrences and intensity as related to solar activity, while other research discusses the impact climate change may have on these storms....
Simulation of Wireless Network Systems
This chapter deals with simulation of wireless network systems. We introduce the basics of discrete-event simulation as it is the simulation technique that is used for simulating wireless networks. We then review the main characteristics of the commonly used stochastic distributions used for the simulation of wireless networks. The techniques used to generate and test random number sequences are investigated. Then, we introduce the techniques used to generate random variates followed by performance metrics considerations.