[sbml-discuss] Re: [Hybrid] Re: Hybrid Models Working Group

Madhukar Dasika m.s.dasika at gmail.com
Thu Sep 2 17:41:52 PDT 2004

hi Dr Salis,

            when you say, combine, both jump and continous markov
processes self -consistently, does it mean that the solution converges
to the determinstic answer in the limit of large N, for the hybrid
model too. What is the metric for self consistency.


On Thu, 2 Sep 2004 09:56:07 -0500, Howard Salis <salis at cems.umn.edu> wrote:
> I'm a bit late to the discussion, but here's my two bits:
> Apart from the computer science definition of discrete/continuous hybrid systems, there is the stochastic process definition of discrete/continuous. For example, Gillespie's SSA algorithm simulates the dynamics of a jump Markov process, a discrete system with discrete transitions. Under certain conditions, you can approximate a jump Markov process as a continuous Markov process, where the state space is continuous and the transitions become continuously occurring as well (but that says nothing about the differentiability of the transitions). Brownian motion, the Wiener process, and several other types of entities/equations are continuous Markov processes.
> For examples of stochastic hybrid algorithms (combining both jump and continuous Markov processes together self-consistently), take a look at Haseltine & Rawlings (2002). I've also submitted a paper to J. Chemical Physics on the topic (an improved algorithm) so keep your eyes peeled.
> Howard Salis

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