## Converging Random Walk

Hello FreeMathHelp,

If we have values 'A' & 'B', and begin at 'A' & end at 'B' over a time series with a defined number of steps, for example:
Value_A =
Value_B =
num_steps = 10

And at each step there is a random process, such as a Weiner process (i.e. P(.5) = x > 0) that causes the value to increase or decrease in a random direction. What is a good way to have it converge to Value_B at the end of 10 steps?

Maybe, count the number of steps that have elapsed (i.e. step_number) and keep track of the number of remaining steps (i.e. num_steps - step_number), then include a term that influences it toward Value_B at each step, ratcheting up the influence the closer it gets to exhausting the total number of steps?

Is there a well-known formula that already does this for discrete data? If so, what is it called and where can I find details on it? If there is not, is this a good way to approach the problem; if not, what is a better approach?

Thanks for any help!

Will