This thesis is concerned with studying what happens when space must be taken into account in discrete stochastic simulation of chemical kinetics. The Stochastic Simulation Algorithm of Gillespie, which is the simulation technique of choice for mesoscopic stochastic chemical kinetics, is rigorously applicable to systems of point molecules which are well-stirred. The former condition means that the molecules must occupy volume negligible compared to the total volume of the system. The latter condition means that the distribution of the molecules' positions in space must be uniformly random.

The SSA has been steadily gaining ground as a method of simulating intracellular kinetics. However, one or both of the conditions which make it rigorously applicable are frequently not met in that biological context. In the first section of this thesis we present our results regarding relaxing the point molecule condition. We find that, even when molecules are allowed to exclude substantial volume, the distribution of inter-collision times is still close to exponential, making the SSA still applicable once appropriate propensity functions are chosen. In the second section of the thesis we concern ourselves with relaxing the well-stirred condition. The Inhomogeneous SSA is applicable in that situation, but it may not be a realistic choice because of its computational cost. We present the Multinomial Simulation Algorithm for stochastic reaction-diffusion, which interlaces approximate stochastic diffusion with reactions simulated according to the SSA.