Limiting Approximations for Stochastic Processes in Biochemical Systems

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  Limiting Approximations for Stochastic Processes in Biochemical Systems
  Casper Woroszylo
  Interest in stochastic modeling of biochemical processes has increased over the past two decades due to advancements in computing power and an increased understanding of the underlying biology. The Gillespie algorithm is an exact simulation technique for reproducing sample paths from a continuous-time Markov chain. However, when spatial and temporal time scales vary within a given system, a purely stochastic approach becomes intractable. In this work, we discuss two types of hybrid approximations, namely piecewise-deterministic and quasi-equilibrium approximations. These approaches yield strong approximations for either the entire biochemical system or a subset of the system, provided the purely stochastic system is appropriately rescaled.