Instantaneous state

of a homogeneous Markov chain with a countable set of states

A state (say, $i$) for which the density of the transition probability,

$$a_{ii}=\lim_{h\downarrow0}\frac{p_{ii}(h)-1}{h},$$

where $p_{ii}(h)$ is the probability of transition from $i$ to $i$ in time $h$, is equal to $-\infty$. In the opposite case the state $i$ is called non-instantaneous, or retarded.

References

[1]	I.I. [I.I. Gikhman] Gihman, A.V. [A.V. Skorokhod] Skorohod, "The theory of stochastic processes" , 2 , Springer (1975) (Translated from Russian)

References

[a1]	D. Williams, "Diffusions, Markov processes, and martingales" , 1 , Wiley (1979)
[a2]	K.L. Chung, "Markov chains with stationary transition probabilities" , Springer (1967)
[a3]	E.B. Dynkin, "Markov processes" , 1 , Springer (1965) (Translated from Russian)
[a4]	D. Freedman, "Brownian motion and diffusion" , Holden-Day (1971)