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In probability theory, what's the difference between a subordinator and a compensator?

A subordinator is a Lévy process of a special type It's a positive, not decreasing process, which starts at 0For example a Gamma process.A compensator is a really different process For a given a given Finite variation process with locally integrable variation A(t) you define the compensator of A(t) as the unique PREDICTABLE process A'(t) that make A(t)-A'(t) a local martingale. For exemple if you take the Poisson process its compensator is simply f(t)=t, because N(t)-t is a martingale.The fact that it is unique is certainly not trivial.

So it's kind of like subtracting away the drift of a F.V. process to make it a martingale ? (compensator).

Yep That's the definition you can find in Protter's book page 118.A beautiful book not for beginner's though because of the sometime too short proofs which lack explaination sometimes (my opinion)

Mine's on p.119 (2nd ed v2.1).What do you know about stochastic processes with jumps?Also, what have semigroups got to do with Feller processes?Thanks,

Feller processes are defined with a semigroup operator ( in the functional sense i.e. for conitnuous bounded fuctions with compact support or something like that ) with special properties ( continuity in 0, contraction,etc) from which you can derive a probability transition semigroup For stochastic processes with jumps, Lévy processes provide a good deal of examples but of course not the general case for example you can have processes with jumps that are not independent and stationnary

Thanks!

As you know from your topic on Markov processes, if (X_t) is such a process then for each function f there is a function g such that E(f(X_(t+s))|F_s)=g(X_s) ; the function g depends linearly upon f and we denote by P_t the corresponding linear operator : g=P_t f. There's a different P_t for each "time-step" t and the family (P_t) of operators satisfies P_t P_s=P_(t+s) (Chapman-Kolmogorov equation), which is why we term it a "semi-group" of operators.A Feller process is a Markov process whose semi-group acts nicely on a class of smooth functions (namely continuous functions vanishing at infinity). This allows one to talk about cadlag modifications, the infinitesimal generator of the process (the "derivative" of the semi-group at t=0), Kolmogoroff equations, etc.Most "natural" Markov processes are Feller, including Lévy Processes and "nice" functions of them.

thx moltabile a much better explanation than mine

Not that much better TheBridge ; you were right to mention that a larger class of jump processes than just Levy processes are Feller processes and are applicable to, say, financial modelling (among other things).

Yes, I've just been reading the D. Duffie, D. Filipovic, and W. Schachermayer paper on Affine Processes (Annals of Applied Probability, 2003) which gives some theory and application of Feller and Markov processes and semigroups in finance. (That's quite some paper!)