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Math Help - Probability over time of a 2D random walk escaping a circle

  1. #1
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    Probability over time of a 2D random walk escaping a circle

    Imagine a circle with radius of 120 pixels. In the centre of the circle is a square cursor (10x10pixels). every 0.02 seconds the cursor's position moves on both the x and y axis a random amount of pixels (mean = 0 standard deviation = 3).

    What is the probability over time that the cursor will exit the circle?

    I have simulated this and derived the probability that way, but would really like to know if there's a better way to determine the probability of exit for a given amount of time-elapsed.

    Thanks for your help!
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  2. #2
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    Re: Probability over time of a 2D random walk escaping a circle

    I think this is covered in the stokes-einstine equation for the diffuffusion of particles in solution/suspension. try there.
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