Hello.
I have this problem. It is modeling high-frequency financial data.
The gamma OU process X (t), BDLP compound Poisson with intensity h > 0
and
E(a) exponential (a) distribution of jump. Lévy density w of Z (1):
w(x) = ahexp(-ax), x is more or equal than 0,
f(R) < infinity,
g(z) = izh/(a-iz).
OUCP rejection sampling
x(t) = x(0)exp(-ct) + suma(0<t(j)is less or equal to
T)[z(j)exp(t(j)-ct)],
cf. shot noise Cox process, 0 < t1 < .. < tk is less or equal to T jump
times of BDLP Z,
z(j) jumps.
Let
B = max (0<t<T)[x(t)] = max (1<j<k)[[x(0) + suma(l goes from 1 to
j)z(l)exp(t(l))]exp(-t(j))],
simulate Poisson (BT) = m, then m uniform points on [0,T].
Each point s is let with probability x(s) / B, 0 < s1 < s2 < ....... sn
< T, n < m.
Could you please help me to simulate this process? I hope that it is
possible to do it in R.
Thanks in advance
Barbora Kocurova
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