Conditioning continuous-time Markov processes by guiding

A continuous-time Markov process X can be conditioned to in a given state at fixed time T>0 using Doob's h-transform. This transform requires the typically intractable transition density of X. The effect h-transform described as introducing guiding force on process. Replacing this with an approximation defines wider class guided processes. For certain approximations law approximates – and is equivalent actual conditional distribution, tractable likelihood-ratio. main contribution paper prove that principle process, introduced [M. Schauer, F. van der Meulen, H. Zanten, Guided proposals for simulating multi-dimensional diffusion bridges, Bernoulli 23 (2017a), pp. 2917–2950. doi:10.3150/16-BEJ833] stochastic differential equations, extended more general In particular we apply technique jump processes discrete spaces. perspective enables us improve upon existing results hypo-elliptic diffusions.