This book highlights the applications of stochastic differential equations in white noise probability space to chemical reactions that occur in biology. These reactions operate in fluctuating environments and are often coupled with each other. The theory of stochastic differential equations based on white noise analysis provides a physically meaningful modelling framework. The Wick product-based calculus for stochastic variables is similar to regular calculus; therefore, there is no need for Ito calculus. Numerical examples are provided with novel ways to solve the equations. While the theory of white noise analysis is well developed by mathematicians over the past decades, applications in biophysics do not exist. This book provides a bridge between this kind of mathematics and biophysics.
Chapter
1. Introduction to Chemical transformations in far from
equilibrium systems.
Chapter
2. A brief introduction to vectors spaces:
succinct but pertinent summary for scientists.
Chapter
3. White noise
probability spaces (Hermite polynomials and functions and their use in
defining Weiner Chaos expansion).
Chapter
4. Introduction to Skorohod
integration and Malliavian derivativespractical interpretations.
Chapter
5.
Introduction to Wick Product and its algebra (analytical solutions to Wick
product driven stochastic differential equations; Hermite transformations).-
Chapter
6. Numerical solutions to stochastic chemical reactions.
Chapter
7.
Stochastic coupled reactions systems: Numerical solutions.
Chapter
8.
Modelling chiral symmetry breaking and stability in a noisy environment using
Wick productsA case study.
Don Kulasiri holds a chaired professorship in Computational modelling and systems biology at Lincoln University, New Zealand, during the last 25 years, and he has been an academic over 33 years. He obtained his B.Sc. (Honours) in mechanical engineering at University of Peradeniya, Sri Lanka, in 1980, and M.S. and Ph.D. at Biological Systems Engineering department, Virginia Tech, USA, in 1988 and 1990, respectively. He has been a visiting professor or a visiting scholar to Princeton University(2004, 2006), Stanford University(1998), USA, and Oxford University(since 2008), UK. His research has been ranked A (world class) by the New Zealand government panels for the last 21 years, and he has graduated over 58 Ph.D. and 15 masters students and authored more than 200 publications including 6 research monographs, 1 edited book and 1 edited proceeding. He founded (1999) and directs the Centre for Advanced Computational Solutions (C-fACS) at Lincoln University.
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