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Math Help - Updating position distribution using velocity distribution---convolution problem (?)

  1. #1
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    Updating position distribution using velocity distribution---convolution problem (?)

    Hi:

    Say I have a normalized distribution function that defines the likelihood of an object having some (x,y) position at time t. That is p(x,y,t) is the probability that the object is located at (x,y) at time t. I also have a normalized distribution function that defines the likelihood of this same object having some (vx, vy) velocity at time t. That is, p(vx,vy,t) is the probability that the velocity vector of this object is defined by (vx,vy). Say I know p(x,y,t), p(vx,vy,t) and p(vx,vy,t+dt). That is, I know the position distribution and velocity distribution at time t, as well as the velocity distribution at time t+dt. How do I advance the position distribution to p(x,y,t+dt)? Is this a convolution process? I'm really not sure how to approach the problem.

    Thanks.
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  2. #2
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    Re: Updating position distribution using velocity distribution---convolution problem

    Hey easyshare.

    You could use a convolution process to discuss addition of increments, however the convolution only works when all variables being "summed" are independent.

    Are you sure you can make the increments (the "dt" as a vector) independent as good assumptions?
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