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## Main Question or Discussion Point

Hello there,

I am wondering if somebody could help in an issue far from my expertise.

I have some data which is reasonable to conjecture could be modelled with a random walk with drift.

I am struggling though to understand how to estimate from the empriic data the most likely drift and variance value necessary to simulate the random walk.

So far I thought about this possible method.

1) From the empiric data estimate the hitting time to a conventional value for each available experimental path.

2) As hitting times are distributed according to a Inverse Gaussian distribution, I could use the data from 1) to estimate the Inverse Gaussian parameters using standard Maximum Likelihood estimators

3) From calcualtion at 2) I should be able to estimate drift and variance as theory tells us how they relate to the Inverse Gaussian parameters.

Any comment on this? Any suggestion? Many thanks in advance

Best Regards

I am wondering if somebody could help in an issue far from my expertise.

I have some data which is reasonable to conjecture could be modelled with a random walk with drift.

I am struggling though to understand how to estimate from the empriic data the most likely drift and variance value necessary to simulate the random walk.

So far I thought about this possible method.

1) From the empiric data estimate the hitting time to a conventional value for each available experimental path.

2) As hitting times are distributed according to a Inverse Gaussian distribution, I could use the data from 1) to estimate the Inverse Gaussian parameters using standard Maximum Likelihood estimators

3) From calcualtion at 2) I should be able to estimate drift and variance as theory tells us how they relate to the Inverse Gaussian parameters.

Any comment on this? Any suggestion? Many thanks in advance

Best Regards