Routines for simulating paths of stochastic processes: random walk, Poisson process, Brownian motion and their multidimensional versions, as well as birth-and-death processes, branching and reproduction models. See

http://www.math.uu.se/research/telecom/software/

2002; birthdeath.m, bm3plot.m, brownian.m, galtonwatson.m, moran.m, poisson2d.m, poisson3d.m, poissonjp.m, poissonti.m, ranwalk2d.m, ranwalk3d.m, ranwalk.m, README, rw3plot.m

comment: Intuitive, but not the most efficient way of programming.

Ref.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=2493&objectType=file

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a 2-Dimensional Random Walk process program in matlab.

comment: A couple remarks for this homework solution:

– several (most!) variables are never used (T,s,t, mx,my,mr)

– explain what the input variable n is in the help, because not « any value of time n » is valid. (it can be a positive integer only!)

– add an error check for that in the code

– The help can be improved. Explain what the user may expect (a plot!).

– why not return both X and Y?

– Have you actually typed « help two_D_Rand_walk »? What you get is not very informative for the user, isn’t it? Or do you want a lot of emails 😉

Ref.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=14864&objectType=file

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http://ocw.mit.edu/OcwWeb/Biological-Engineering/20-011JSpring-2004/Simulations/

# Simulations

Monte Carlo (PDF)

Matlab Tutorial (PDF)

*PCR simulator*

pcr_sim.m (M)

Replicate a certain number of starting copies of DNA for several cycles. Try different probabilities of replication to get different histograms showing how much DNA is produced over many trials.

pcr_sim.fig (FIG)

Put this in the same directory as pcr_sim.m to be able to run « pcr_sim » from the matlab prompt.

Random Walk – 2D with 2 Particles (M)

Look at how these simulations work and try making your own 3D random walk or have your particle trace out a trajectory in Matlab.

Lab

Random Walk – 2D (M)

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———-tutorial of Matlab (first approach for dummies) , exemple walk 1D:

web.mit.edu/14.451/www/**Matlab**_Tutorial.pdf

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