# Markov Jump Process - Transition Probabilities

For the transition probability of a Markov jump process from state $$x$$ to $$y$$ in a small time interval $$\Delta t$$, what is the meaning of $$o(\Delta t)$$? $$\alpha$$ is a constant $$\in[0,1)$$.

That is expressing the fact that the probability to have two or more jumps in the time $$\Delta T$$ is negligible with respect to $$\alpha \Delta t$$, and this fact is expressed in the little o notation.
It could also be expressed in "Big O notation" as $$\alpha \,\Delta t + O\left( {\Delta t^2 } \right)$$