Simulation plays an important r^ ole in stochastic geometry and related elds, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribution of a Markov chain such as a spatial birth-and-death process. The samples usually fail to be exact...

Gánti's chemoton model is an illustrious example of a minimal cell model. It is composed of three stoichiometrically coupled autocatalytic subsystems: a metabolism, a template replication process, and a membrane enclosing the other two. Earlier studies on chemoton dynamics yield inconsistent results. Furthermore, they all appealed to deterministic simulations, which do not take into account the...

In order for scientists to learn more about molecular biology, it is imperative that they have the ability to construct accurate models that predict the reactions of species of molecules. Generating these models using deterministic approaches is not feasible as these models may violate some of the assumptions underlying classical differential equations models (e.g., small populations with discr...

The small number of some reactant molecules in biological systems formed by living cells can result in dynamical behavior which cannot be captured by traditional deterministic models. In such a problem, a more accurate simulation can be obtained with discrete stochastic simulation (Gillespie’s stochastic simulation algorithm – SSA). Many stochastic realizations are required to capture accurate ...

We present a stochastic approach for the simulation of coagulation-diffusion dynamics in the gelation regime. The method couples the mass flow algorithm for coagulation processes with a stochastic variant of the diffusion-velocity method in a discretized framework. The simulation of the stochastic processes occurs according to an optimized implementation of the principle of grouping the possibl...

In this paper one of the important “end of life options” (remanufacturing) has been analysed. Among the related studies surveyed the various remanufacturing aspects, less attention has been paid to the stochastic process routing. In this regard, a remanufacturing process routing with stochastic activities is modelled as a GERT network. One of the efficient ways to analyse a remanufacturing proc...

A growing realization of the importance of stochasticity in cell and molecular processes has stimulated the need for statistical models that incorporate intrinsic (and extrinsic) variability. In this chapter we consider stochastic kinetic models of reaction networks leading to a Markov jump process representation of a system of interest. Traditionally, the stochastic model is characterized by a...

Article history: Received 7 August 2009 Received in revised form 4 December 2009 Accepted 20 January 2010 Available online 28 January 2010

Stochastic simulation of complex biochemical networks is a topic of current interest, in spite of the importance of the Gillespie algorithm it requires substantial amount of computational effort to simulate a complex system, Many algorithms are available now to control the two most important parameters in simulation: speed and accuracy. It can be proved that the stochastic modelling approach pr...

A lot of discrete approximation schemes for stochastic differential equations with regard to mean-square sense were proposed. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We will propose another type of error analysis. Also we will show results of simulation studies carried out for these schemes...