Epidemic Modeling: SIRS Models (short) - Columbia University

Large Deviations Principle
Def. Family µ N satisfy LDP on X with rate
function I if
− inf I(x) ≤ lim 1
x∈F ◦ N→∞
N log µN (F )
1
≤ lim N→∞
N log µN (F ) ≤ − inf I(x)
x∈ ¯F
for F ⊂ X .
Y t = Poisson processes rate m
y N t
= N −1 Y Nt satisfy LDP with rate function
I(y) =
:=
∫ T
(ẏt )
0 ẏt log
m
∫ T
0 f(ẏ t, m) dt
− ẏ t + m dt
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