Usage of additive and multiplicative noise

[Jeriffer Smith]

Dear TVBers,

    I'm so sorry to bothor you again. I wonder what's the difference between additive and multiplicative noise.

   Which conditions or models prefer additive noise and which ones fit multiplicative noise? Is it necessary to choose the kind of noise?

   Thanks for your time!

Best Regards,

Jeriffer

[WOODMAN Michael]

hi

It's a convention in stochastic differential equation literature to refer to distinguish between noise level which depends on the state variables as "multiplicative" and noise level independent of state variable values as "additive".  Concretely, in a Euler-Maruyama scheme, it's the difference between

X_t+1 = X_t + dt f(X_t, t) + dW_t sqrt(dt) g(X_t, t) is called multiplicative

while

X_t+1 = X_t + dt f(X_t, t) + dW_t sqrt(dt) g(t) is called additive

Note the difference in the noise scaling function g. 

It's appropriate to start with additive until your modelling question requires the extra complication of state-dependent noise.  Most TVB papers use the former while some use the latter, e.g. https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002634. 

cheers,

Marmaduke

---

From: tvb-...@googlegroups.com <tvb-...@googlegroups.com> on behalf of Jeriffer Smith <jeriffe...@gmail.com>
Sent: Monday, March 21, 2022 1:47:32 PM
To: TVB Users
Subject: [TVB] Usage of additive and multiplicative noise

 

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[Jeriffer Smith]

Thank you so much for your help!