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I have run into this problem, and being that I know nothing about stochastic DiffyQ I am trying to toy around with it. Basically, the following is a boiled down version of my problem:

I have a probability density function that is given: p(t)

and let's say we pick 1 value from that density function (so that we get some value of time). I'm not exactly sure the proper notation for how to write the question, so the random variable that goes by the pdf p(t) i will call P. So then I will have a diffyQ that looks like this

[itex]\frac{dV(t)}{dt}=-V(t)+\delta (t-P)[/itex]

where P is the time which is pulled from that probability distribution. My inuition tells me that I should get some probability distribution for V at every time. Is there a way to get that?

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# Stochastic ODE

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