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Identify this mathematical expression !!

hi guys, I have a mathematical expression here, could someone identify the name of the topic it falls under, or if someone is familiar with this expression (any keyword?) could you tell me what exactly it is?

Attachment 26868

Here Ht is a state variable. Guys who familiar with optimization problem should well know that it is usually assumed the state variable is continuous and smooth, e.g., the motion of capital in the optimal growth model. However, I want to assume the state Ht response to control variable Rt conditionally. I want to search in google whether others have such an assumption in their academic paper but I did not know what is the 'exact expression' of this 'conditional motion'. I tried "nonsmooth motion of state variable", "kinked state variable" but it seems those expressions are not accurate.

Any suggestion and help is appreciated. Thank you.

Re: Identify this mathematical expression !!

Hey DavidL.

This sounds a lot like a finite recurrence relationship:

Finite difference - Wikipedia, the free encyclopedia

Re: Identify this mathematical expression !!

Hi chiro, thanks for you reply.

Finite difference is an approximation of derivative. However, in my expression, the value of the derivative alpha is conditional on the sign of changes of dependent variable Rt. If the change of Rt is negative, the derivative alpha is set to zero while it is positive, say alpha=0.5 if the change of Rt is positive.

Re: Identify this mathematical expression !!