# Does the time between prices created from a GBM affect the estimation of parameters of the GBM?

Recently I created a simulation of a GBM. The time between the prices were sampled from an exponential distribution. The log rate of return was sampled from $\sigma \sqrt { { t }_{ i }-{ t }_{ i-1 } } { Z }_{ i }+(\mu -\frac { { \sigma }^{ 2 } }{ 2 } )({ t }_{ i }-{ t }_{ i-1 })$ where ${ Z }_{ i }\sim N(0,1)$.

When I estimated the drift of prices from the simulation without using the time between the prices, I was able to get back the drift I programmed into the simulation.

So I concluded that the time between prices doesn't affect the estimation of parameters of a GBM.

Is this conclusion correct?

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