[R] simulation of compound Poisson and Cox process

[Barbora Kocúrová]

	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. Lévy 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