[nalzok]

Is this equivalent to treating the linear recurrence as a convolution and computing it with a Fourier transform? See https://www.youtube.com/watch?v=OpJMn8T7Z34&t=840s

[rkp8000]

I had the same thought. If a were constant I believe the solution would just be a convolution of b_t with an exponential filter. I think this is different because a_t depends on time, so it's equivalent to convolving b_t with a filter whose timescale changes at every timestep, which doesn't seem like something that's obviously parallelizable with FT.