solve fractional fuzzy stochastic differential equation

anyone knows how to create a model of fuzzy fractal Brownian motion when hurst parameter is NOT equal to 0.5 in Matlab.

Answer 1

[WEI-MIN SHEN]

1 deal with the stochastic process with either Volterra or Harmonizable representation

2 select any type of stochastic calculus to solve your SODE

3 (for numerical simulation) you may need to involve some special orthogonal series to approach

4 discretize the SODE and solve in either integral or differential form

Simply, the main different between Bm and fBm is the smoothness of the trajectory (we also interpret as the accelerate/decelerate regon which the particle jump into)

If you just want a quick, there is a inbuild function to generate fBm called "wfbm"

For any mistake/misunderstanding, feel free to correct me

wm

[George Urumov]

thats really helpful! thank you. what is the function to fuzzify paramerers such as Hurst exponent and others?

[George Urumov]

I think for fractal Brownian Motion need to use Benoit (http://www.trusoft-international.com/). have you tried it and if yes how did you implement it in Matlab?

Answer 2

[Image Analyst]

I don't know what that means but I have attached some random walk demos if you want those.

[George Urumov]

so random walk is basically brownian motion that is martingale with hurst equal to 0.5. i am after fractal brownian motion that i want to fuzzify as well.

[Image Analyst]

I don't know what that means, but I don't need to. So, OK, good luck. Hopefully this gave you a good chunk of code to start with. Chances are that no one has such a very specific, esoteric program and if there is, they won't stumble across your question. So you'll have to finalize the code yourself. Again, have fun and good luck.