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Research Report SRR95-019
On the simulation of biological diffusion processes
Henry C. Tuckwell and Petr Lansky
Abstract:
Many phenomena of interest in biology can be modeled using diffusion
processes satisfying
a stochastic differential equation. A stochastic differential equation,
representing a
population growth process, is simulated using both a strong Euler scheme
and a weak
scheme. It is found that there are no significant differences between the
results
obtained at a particular value of the time step, but that the weak scheme
only takes
about 20% of the CPU time taken by the strong scheme. It is concluded that
in the
majority of simulations of biological diffusion processes it is
advantageous to employ a
scheme involving Bernoulli rather than Gaussian random variates because it
involves far
fewer machine arithmetic operations.
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