**R. P. Agarwal, S. Hristova, D. O'Regan, P. Kopanov**

##
*p*-Moment Exponential Stability of Differential Equations with Random
Impulses and the Erlang Distribution

**abstract:**

The investigation of differential equations with random impulses combines ideas
in the qualitative theory of differential equations and probability theory. The
*p*-moment exponential stability of the solutions is defined and studied
when the waiting time between two consecutive impulses is Erlang distributed.
The study is based on the application of Lyapunov functions. Some examples are
given to illustrate the results.

**Mathematics Subject Classification:**
34F05, 60G17, 34A37, 34D20, 93E15

**Key words and phrases:** Impulsive differential equations, random moments
of impulses, Erlang distribution, $p$-moment exponential stability