Moving average filter for MC solution of PDE

[kai_sikorski]

I have a PDE that can be interpreted as basically an exit time problem for a certain stochastic process. I would like to use this to verify an analytical solution I've found. If I start the stochastic process at (x,y), then the average exit time from a certain region will be equal to the value of the solution of the PDE I care about at (x,y).

I could divide up my region into a discrete set of points and find the average for each of those. However that wastes some of the data because, say I start the process at x₀, y₀. During the next time step the position is x₁, y₁, and so if the total exit time is T then not only do I have the data point

x₀, y₀, T

but also

x₁, y₁, T - dt

However x₁, y₁ is probably not exactly one of any predefined start points I defined.

So what I would like to do is take the whole list of data

{ { x₀, y₀, T}, {x₁, y₁, T-dt}, {x₂, y₂, T- 2 dt}, ... }

And apply a moving average filter. Is there a built in method for doing this in Matlab or Mathematica? I can find documentation for things like the filter2 command in Matlab, this seems to apply more to a case where your data is indexed by a discrete sets of points so that you can arrange it in for example a matrix. That's not the case here where the data is basically indexed by floats.

 

[mmwave]

Thank you for sharing your problem with us. It sounds like you have a very interesting and complex PDE to work with. To verify your analytical solution, you have proposed using a moving average filter on your data set. While there may not be a built-in method specifically for this in Matlab or Mathematica, there are some approaches you can try.

One option is to use the "interp1" function in Matlab to interpolate your data onto a regular grid, which can then be used with the "filter2" command. This may require some preprocessing of your data to convert it into a format that can be interpolated.

Another option is to use the "smoothdata" function in Matlab, which allows you to apply various smoothing techniques to your data, including moving average filters.

In Mathematica, you can use the "MovingAverage" function to apply a moving average filter to your data. You can also use the "Interpolation" function to interpolate your data onto a regular grid, which can then be used with the "MovingAverage" function.

I hope these suggestions are helpful to you. Good luck with your research!