@PhDThesis{	  itlic:2006-007,
  author	= {Stefan Engblom},
  title		= {Numerical Methods for the Chemical Master Equation},
  school	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2006},
  number	= {2006-007},
  type		= {Licentiate thesis},
  month		= sep,
  day		= {27},
  copies-printed= {80},
  pages		= {112},
  note		= {Included papers available at
		  \url{http://www.it.uu.se/research/publications/lic/2006-007/paperA.pdf},
		  \url{http://www.it.uu.se/research/publications/lic/2006-007/paperB.pdf},
		  and
		  \url{http://www.it.uu.se/research/publications/lic/2006-007/paperC.pdf}}
		  ,
  abstract	= {The numerical solution of chemical reactions described at
		  the meso-scale is the topic of this thesis. This
		  description, the \emph{master equation of chemical
		  reactions}, is an accurate model of reactions where
		  stochastic effects are crucial for explaining certain
		  effects observed in real life. In particular, this general
		  equation is needed when studying processes inside living
		  cells where other macro-scale models fail to reproduce the
		  actual behavior of the system considered.
		  
		  The main contribution of the thesis is the numerical
		  investigation of two different methods for obtaining
		  numerical solutions of the master equation.
		  
		  The first method produces statistical quantities of the
		  solution and is a generalization of a frequently used
		  macro-scale description. It is shown that the method is
		  efficient while still being able to preserve stochastic
		  effects.
		  
		  By contrast, the other method obtains the full solution of
		  the master equation and gains efficiency by an accurate
		  representation of the state space.
		  
		  The thesis contains necessary background material as well
		  as directions for intended future research. An important
		  conclusion of the thesis is that, depending on the setup of
		  the problem, methods of highly different character are
		  needed.}
}