Notation

DRI	directly Riemann integrable
a.s.	almost surely
i.i.d.	independent identically distributed
r.v.	random variable/random variables
d.f.	distribution function
B-G-W	Bienaymé-Galton-Watson
MRP	Markov renewal process
SMP	semi-Markov process
	set of non-negative integers, i.e. {0, 1, 2, …}
	set of positive integers, i.e. {1, 2, …}
	set of integers, i.e. {… −2, −1, 0, 1, 2, …}
	set of rational numbers
	set of real numbers
	set of non-negative real numbers [0, ∞)
	set of complex numbers
log	natural logarithm
	set [−00, 00]
o(x)	small 0 of x in 0, i.e. lim o(x)/x = 0
O(x)	big O of x in 0, i.e. O(x)/x is bounded in a neighborhood of 0
l_d	d-dimensional vector whose components are all 1
I_d	identity matrix of order d
diag(a_i)	diagonal matrix whose ith diagonal entry is a_i,
(E)	set of all subsets of E
	σ-algebra
σ(C)	σ-algebra generated by C
(E)	σ-algebra of Borel sets of a topological space E
	probability measure
	probability space
	expected value (mean)
ar	variance
ov	covariance
δ_ω	Dirac measure in ω, i.e. δ_ω(A) =
	indicator function of a set A, i.e.