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5

As far as I can tell from the problem description you can simply shuffle the list as many times as needed, since duplicate permutations are allowed: (* thanks ybeltukov for tweaks *) f[n_, m_] := Table[RandomSample @ #, {m}] & @ Range @ n Example: f[5, 3] {{5, 3, 1, 4, 2}, {3, 4, 2, 5, 1}, {2, 1, 5, 3, 4}}


4

mrandomperms[n_, m_]:= Table[PermutationList[RandomPermutation[n]], {m}] Was my initial answer, but, as pointed out by Mr. Wizard, PermutationList should be given $n$ as a second argument, since otherwise it will give the wrong answer if $n$ is a fixed point. Also, Table can be eliminated for elegance and efficiency, leaving one with: mrandomperms[n_, ...


0

This an answer of question 2, "How to recover the simulated values of the random variable?": Just specific the random variable in the state vector argument. For example, mysde[q_, I1_, n0_, sd_] := ItoProcess[ {\[DifferentialD]n[t] == ( -q n[t]) \[DifferentialD]t + I1 \[DifferentialD]t + \[DifferentialD]w[t]}, {n[t], I1 + w[t]}, {n, n0}, t, w ...


4

The documentation says that you can use the ProcessEstimator options ... but it does not say which one you can use I take exception to this statement. The documentation for FindProcessParameters clearly states two things. Option values Automatic, "MaximumLikelihood", and "MethodOfMoments" can be given generally as values for the option ...


11

Mathematica's estimation routines are able to recover the Hurst exponent from the sample: BlockRandom[SeedRandom["mathematica.SE/58539"]; tlow = 1; thigh = 1000; tinc = 1; hurst = 0.4; dataz = RandomFunction[FractionalBrownianMotionProcess[hurst], {tlow, thigh, tinc}, 1]]; FindProcessParameters[dataz, FractionalBrownianMotionProcess[h]] {h -> ...



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