The nature of statistical learning theory
The nature of statistical learning theory
On the q-analogues of the Zassenhaus formula for disentangling exponential operators
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on special functions and their applications
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
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The fine-scale stochastic behavior of genetic regulatory networks is often modeled using stochastic master equations. The inherently high computational complexity of the stochastic master equation simulation presents a challenge in its application to biological system modeling even when the model parameters can be properly estimated. In this article, we present a new approach to stochastic model simulation based on Kronecker product analysis and approximation of Zassenhaus formula for matrix exponentials. Simulation results on model biological systems illustrate the comparative performance of our modeling approach to stochastic master equations with significantly lower computational complexity. We also provide a stochastic upper bound on the deviation of the steady state distribution of our model from the steady state distribution of the stochastic master equation.