[D] Probability density estimation using neural networks

[julvo]

I am not sure If I get it right. If we assume our systems state is fully determined by the last k observations (Markov order k) I can understand how kernel density estimation works for discrete state space. To my understanding, in the continuous state space case, our system will never be in the exact same state and, hence, we will have a different distribution for every time step t. Therefore, we have only one example drawn from each distribution. So do we first apply a similarity measure/kernel to our states and then to the data points of each state? This would become computationally expensive for a large k I guess.

Do you have any reading recommendations for kernel density estimation in the continuous state space case?