View source for Instantaneous state

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''of a homogeneous [[Markov chain|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====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  I.I. [I.I. Gikhman] Gihman,   A.V. [A.V. Skorokhod] Skorohod,   "The theory of stochastic processes" , '''2''' , Springer  (1975)  (Translated from Russian)</TD></TR></table>



====Comments====


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