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A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the… (More)

- David F. Anderson, Gheorghe Craciun, T. G. Kurtz
- Bulletin of mathematical biology
- 2010

We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state… (More)

- David F. Anderson, Desmond J. Higham
- Multiscale Modeling & Simulation
- 2012

We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute… (More)

- David F. Anderson
- The Journal of chemical physics
- 2007

Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce… (More)

- David F. Anderson
- SIAM Journal of Applied Mathematics
- 2008

We consider a class of nonlinear differential equations tha t arise in the study of chemical reaction systems that are known to be local ly asymptotically stable and prove that they are in fact… (More)

- David F. Anderson
- SIAM J. Numerical Analysis
- 2012

We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method… (More)

Let R be a commutative ring with Nil(R) its ideal of nilpotent elements, Z(R) its set of zero-divisors, and Reg(R) its set of regular elements. In this paper, we introduce and investigate the total… (More)

We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is… (More)