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Semi-groupes et mesures invariantes pour les processus semi-markoviens à espace d'état quelconque
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jacod, Jean |
| Copyright Year | 1973 |
| Abstract | Let be a jump process, with values in a measurable space (E, ~). We denote by U, the time between t and the last jump before t, and by Vt the time between t and the first jump after t. (Zt) is called a semiMarkov process of the first, second or third kind, if (Zt, U,, Vt), (Zt, Ut) or (Zt, Vr) is a Markov process. The (random) set of discontinuity points of Z, is denoted by N. Nd(Ng) is the set of right (left) limit points of N. We suppose that Nd c Ng and that for any t the probability for t to be in Nd is zero. Under these assumptions, we examinate the relation between the three different kinds of semi-Markov process. We give a characterization for the transition semi-group of the Markov process (Z,, Ut, Vt), (Zt, U t) or Vt) according to the kind of the semi-Markov process (Zt). We give the form of invariant measures for these processes when they are recurrent. At last we examinate what happens when the assuption Nd c Ng is replaced by the assumption Nd = Ng. INTRODUCTION Les processus semi-markoviens (en abrégé : PSM) sont définis ainsi : étant une fonction aléatoire a valeurs dans un espace mesurable (E, ~), on pose Ut = t si pour tout t], Ut = t sup (s t, Zt) Annales de 1’Institut Henri Poincae Section B Vol. IX, n° 1 1973. Vol. IX, n° 1, 1973, p. 77-1 t2. |
| Starting Page | 77 |
| Ending Page | 112 |
| Page Count | 36 |
| File Format | PDF HTM / HTML |
| Volume Number | 9 |
| Alternate Webpage(s) | http://www.numdam.org/article/AIHPB_1973__9_1_77_0.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
