Of nature of Pereism there is a lot to say, just as much as about any 
other philosophy that deals with ethics of life. Reading this one must 
take notice, that this text shall be devoid of Mysteriorum Aleph Crucis. 
Then, what is Pereism, what constitutes it? In most compact terms it could 
be called an eclectic of Stoicism, Fatalism, and a notion of constant 
decline of all things, which I like to call Decadence. In order to make 
this short description a bit more intuitive and readable i am going to 
cite three passages of Encheiridion of Epictetus, which are as follows:

"Some things are in our control and others not. Things in our
control are opinion, pursuit, desire, aversion, and, in a word,
whatever are our own actions. Things not in our control are
body, property, reputation, command, and, in one word, 
whatever are not our own actions.", Ench. 1,1

"With regard to whatever objects give you delight, are useful,
or are deeply loved, remember to tell yourself of what general
nature they are, beginning from the most insignificant things.
If, for example, you are fond of a specific ceramic cup, remind
yourself that it is only ceramic cups in general of which you
are fond. Then, if it breaks, you will not be disturbed.
If you kiss your child, or your wife, say that you only kiss 
things which are human, and thus you will not be disturbed if
either of them dies." Ench. 3

"Men are disturbed, not by things, but by the principles and
notions which they form concerning things. Death, for instance,
is not terrible, else it would have appeared so to Socrates."
Ench. 5,1,1-2

I think the words of Epictetus have covered the Stoicism part
of Pereism, now onto the Fatalism.
Fatalism is the simpler concept, that needs less coverage than
the Stoicism. The idea is thus, that all things are going to
irrevocably meet their fate, despite any circumstances.

The concept of Decadence is closely coupled with Fatalism,
in a way that all is going to perish,
thus latin 'pereo' - 'Pereism'. Now, in the Ench. 3, Epictetus
gives an example of death, as that which of all we shall not
fear, yet death is not the only form of decay, that all things
experience. Corpses rot, fruit putrefact, relationships part,
companies break apart, life of each and everything in universe
starts, and then ends at some point, and 'to perish' is the
best verb to describe that notion.

Although Decadence is not exclusive to concept of Death,
I recommend to make it the center of the domain of 
Decadence, in fashion of mediaeval "Memento Mori".

Everything shall perish, and thou hast no need to fret
Omne Peribunt!