FLUCTUATIONS OF SPECTRALLY NEGATIVE MARKOV ADDITIVE PROCESSES By A.E. KYPRIANOU and Z. PALMOWSKI
نویسنده
چکیده
1. Spectrally Negative Markov Additive Processes. This paper presents some fluctuation identities for a special, but none the less quite general, class of Markov Additive Processes (MAP). Before entering our discussion on the subject we shall simply begin by defining the class of processes we intend to work with and its properties. Following Asmussen and Kella (2000) we consider a process X(t), where X(t) = X(t) +X(t), and the independent processes X(t) and X(t) are specified by the characteristics: qij , Gij , σi, ai, νi(dx) which we shall now define. Let J(t) be a right-continuous, ergodic, finite state space continuous time Markov chain, with I = {1, . . . , N}, and with the intensity matrix Q = (qij). We denote the jumps of the process J(t) by {Ti} (with T0 = 0). Let {U (ij) n } be i.i.d. random variables with distribution function Gij(·) (U (ii) ≡ 0). Define the jump process by X(t) = ∑
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