It is well understood that a supercritical continuousstate branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with immigration which initiates subcritical CSBPs (non-prolific mass).Equally well understood in the setting of CSBPs and superprocesses is the notion of a spine or immortal particle dressed in a Poissonian way with immigration which initiates copies of the original CSBP, which emerges when conditioning the process to survive eternally.In this article, we revisit these notions for CSBPs and put them in a common framework using the well-established language of (coupled) SDEs (cf. [7,8,6]). In this way, we are able to deal simultaneously with all types of CSBPs (supercritical, critical and subcritical) as well as understanding how the skeletal representation becomes, in the sense of weak convergence, a spinal decomposition when conditioning on survival.We have two principal motivations. The first is to prepare the way to expand the SDE approach to the spatial setting of superprocesses, where recent results have increasingly sought the use of skeletal decompositions to transfer results from the branching particle setting to the setting of measure valued processes; cf. [26,14,40]. The second is to provide a pathwise decomposition of CSBPs in the spirit of genealogical coding of CSBPs via Lévy excursions in Duquesne and LeGall [10] albeit precisely where the aforesaid coding fails to work because the underlying CSBP is supercritical.1. Introduction. In this article we are interested in X = (X t , t ≥ 0) a continuous-state, finite-mean branching process (CSBP). In particular, this means that X is a [0, ∞)-valued strong Markov process with absorbing state at zero and with law on D([0, ∞), R) (the space of càdlàg mappings from [0, ∞) to R) given by P x for each initial state x ≥ 0, such that P x+y = P x * P y . Here, P x+y = P x * P y means that the sum of two independent processes, one issued from x and the other issued from y, has the same law as the process issued from x + y.
It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description of prolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as the skeleton or backbone of the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP).In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever.Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.
A tanulmány a közfoglalkoztatásban való részvétel okait és a résztvevők által érzékelt előnyöket és hátrányokat vizsgálja, valamint azonosítja a különbségeket a női és a férfi közfoglalkoztatottak tapasztalatai között, továbbá meghatározza azokat az okokat, amiért a közfoglalkoztatási program vonzóbb lehet a nők számára. A tanulmány megírásához 15 közfoglalkoztatottal és három munkafelügyelővel készítettem interjút Komárom-Esztergom és Pest megyében. A női résztvevők a programot egyfajta stratégiai eszközként kezelik, amelynek segítségével összeegyeztethetik a munkát a magánélettel egy olyan kontextusban, ahol a munkaerőpiacra a kiszámíthatatlan munkaidő és a rugalmatlan munkakörülmények jellemzőek. Ennek a stratégiának köszönhetően a nők továbbra is képesek a munka és a magánélet kettős terhét viselni, így a közfoglalkoztatás ahelyett, hogy orvosolná, erősíti a munkaerőpiaci diszkriminációt, elősegíti a kizsákmányolást és fenntartja az ideális munkavállaló normájának társadalmi nemek mentén meghatározott jellegét. A közmunkában a nők aránya egyre jobban növekszik, ami arra utal, hogy a közfoglalkoztatás egy olyan új típusú női munka, amely tolerálja a nők gondoskodási feladatait csakúgy, mint a legtöbb elnőiesedett munka a másodlagos munkaerőpiacon. A női résztvevők úgy érezték, hogy emocionális és szociális előnyben részesülnek annak ellenére, hogy a közmunka egy bizonytalan jellegű foglalkoztatás. Lehetőségeik az elsődleges munkaerőpiacon annyira szűkek voltak, hogy a közfoglalkoztatás számukra felértékelődött. Mivel a munka a férfiak esetében szorosan kötődik a családfenntartó szerephez, valamint a szakmából nyert identitáshoz, a közmunka számukra csak anyagi célt szolgál, és nem kötődik hozzá különösebb jelentés vagy személyes kiteljesülés.
In this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well known for both continuous-state branching processes and superprocesses in the one-type case, so far no such decompositions or even description of prolific genealogies have been given for the multitype cases. Here we focus on superprocesses, but by turning the movement off, we get the prolific backbone decomposition for multitype continuous-state branching processes as an easy consequence of our results.
In this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well-known for both continuousstate branching processes and superprocesses in the one-type case, so far no such decompositions or even description of prolific genealogies have been given for the multitype cases.Here we focus on superprocesses, but by turning the movement off, we get the prolific backbone decomposition for multitype continuous-state branching processes as an easy consequence of our results.
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