65 research outputs found
Large deviations for sums defined on a Galton-Watson process
In this paper we study the large deviation behavior of sums of i.i.d. random
variables X_i defined on a supercritical Galton-Watson process Z. We assume the
finiteness of the moments EX_1^2 and EZ_1log Z_1. The underlying interplay of
the partial sums of the X_i and the lower deviation probabilities of Z is
clarified. Here we heavily use lower deviation probability results on Z we
recently published in [FW06]
Lower deviation probabilities for supercritical Galton-Watson processes
There is a well-known sequence of constants c_n describing the growth of
supercritical Galton-Watson processes Z_n. With 'lower deviation probabilities'
we refer to P(Z_n=k_n) with k_n=o(c_n) as n increases. We give a detailed
picture of the asymptotic behavior of such lower deviation probabilities. This
complements and corrects results known from the literature concerning special
cases. Knowledge on lower deviation probabilities is needed to describe large
deviations of the ratio Z_{n+1}/Z_n. The latter are important in statistical
inference to estimate the offspring mean. For our proofs, we adapt the
well-known Cramer method for proving large deviations of sums of independent
variables to our needs
The Joint IGNTP/INTF Editio Critica Maior of the Gospel of John: its goals and their significance for New Testament scholarship
Conference paper delivered at SNTS Annual Meeting in Halle, Germany, August 200
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst
We consider the behaviour of a continuous super-Brownian motion catalysed by
a random medium with infinite overall density under the hydrodynamic scaling of
mass, time, and space. We show that, in supercritical dimensions, the scaled
process converges to a macroscopic heat flow, and the appropriately rescaled
random fluctuations around this macroscopic flow are asymptotically bounded, in
the sense of log-Laplace transforms, by generalised stable Ornstein-Uhlenbeck
processes. The most interesting new effect we observe is the occurrence of an
index-jump from a 'Gaussian' situation to stable fluctuations of index 1+gamma,
where gamma is an index associated to the medium.Comment: 40 page
Critical Galton-Watson processes: The maximum of total progenies within a large window
Consider a critical Galton-Watson process Z={Z_n: n=0,1,...} of index
1+alpha, alpha in (0,1]. Let S_k(j) denote the sum of the Z_n with n in the
window [k,...,k+j), and M_m(j) the maximum of the S_k with k moving in [0,m-j].
We describe the asymptotic behavior of the expectation EM_m(j) if the window
width j=j_m is such that j/m converges in [0,1] as m tends to infinity. This
will be achieved via establishing the asymptotic behavior of the tail
probabilities of M_{infinity}(j).Comment: 28 page
On the left tail asymptotics for the limit law of supercritical Galton--Watson processes in the Böttcher case
Under a well-known scaling, supercritical Galton-Watson processes converge to a non-degenerate non-negative random limit variable We are dealing with the left tail (i.e. lose to the origin) asymptotics of its law. In the Bötcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing tiny oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the B"ottcher case, we improve a recent lower deviation probability result by describing the precise asymptotics under a logarithmic scaling (Theorem 3). Under additional assumptions, we even get the fine (i.e. without log-scaling) asymptotics (Theorem 4)
Large scale localization of a spatial version of Neveu’s branching process
AbstractRecently a spatial version of Neveu’s (1992) continuous-state branching process was constructed by Fleischmann and Sturm (2004). This superprocess with infinite mean branching behaves quite differently from usual supercritical spatial branching processes. In fact, at macroscopic scales, the mass renormalized to a (random) probability measure is concentrated in a single space point which randomly fluctuates according to the underlying symmetric stable motion process
Large scale localization of a spatial version of Neveu's branching process
Recently a spatial versions of Neveu's (1992) continuous-state branching process was constructed by Fleischmann and Sturm (2004). This superprocess with infinite mean branching behaves quite differently from usual supercritical spatial branching processes. In fact, at macroscopic scales, the mass renormalized to a (random) probability measure is concentrated in a single space point which randomly fluctuates according to the underlying symmetric stable motion process
MPTP-induced degeneration: interference with glutamatergic toxicity
Parkinson's disease (PD) is characterised by the progressive degeneration of nigrostriatal dopamine (DA) neurons resulting in the major symptoms of akinesia and rigidity. Although the primary cause of PD is still not known some features make this disorder a model for neurodegenerative diseases in general. It has been known for some time that symptomatic PD can be attributed to insults with symptoms occurring many years later such as post-encephalitic PD or PD following manganese poisoning. More recently, MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) has been identified as a neurotoxin selective for melanin-containing dopaminergic neurons in humans and non-human primates. The specificity of this neurotoxin and the striking clinical similarities to idiopathic PD, seen in primates, make MPTP-induced parkinsonism the most useful animal model of a neurological disease. There are numerous theoretical possibilities to interfere with both MPTP-induced neurotoxicity and the symptomatology of PD. In recent years excitatory amino acids have gained considerable interest since they can cause excitotoxic lesion of neurons under a number of pathological conditions (Olney et al., 1989; Choi, 1988). Here we summarise the present data and provide new experimental evidence indicating that MPTP-induced degeneration of dopaminergic neurons does involve glutamate-mediated toxicity. It is concluded that glutamate-mediated excitotoxicity results in the destruction of DAergic somata in the substantia nigra. Non-competitive or competitive NMDA antagonists protect nigral neurons from MPTP-induced degeneration whereas their striatal terminals still seem to degenerate
Einige Bemerkungen zum senatorischen cursus honorum vor dem Konsulat
Avtor analizira službeni potek (cursus honorum) legatov onih legij, ki so bile stacionirane v vzhodnih provincah rimskega imperija. Pri tem ugotavlja za senatorske kariere pred konsulatom naslednje. L Zdi se, da do preture nobena služba nima bistvenega vpliva na poznejši službeni potek. Opaziti je samo, da so bili legijski legati že pred to službo v milosti pri vladarju. Mnogi so bili kvestorji, ljudski tribuni, edili ali pretorji kot candidati Augusti ali pa so opravljali službo ab actis senatus. 2. Med preturo in legijskim poveljstvom pridejo v poštev predvsem službe — navadno ena ali dve — legatus proconsulis, iuridicus, praefectus frumenti dandi, curator viae. Niso pa opravljali pred legijskim poveljstvom sledečih služb: namestništvo v pretorskih cesarskih provincah in prefektura cesarske blagajne. Tudi namestništvo v pretorskih senatorskih provincah, ki ga najdemo v dveh primerih, se zdi izjemno. 3. Neposredno napredovanje od legijskega poveljstva v konsulat je redko in nastopi le pri izrednih zaslugah. Če je med legijskim poveljstvom in konsulatom le ena služba, je normalno to namestništvo v cesarski provinci z eno legijo. Vse druge službe so izjemne, kot se zdi. Navadno sta med legijskim poveljstvom in konsulatom dve službi. Za ti dve pridejo v poštev sledeče skupine uradnih mest: guvernerska mesta v cesarskih provincah brez legije, prokonsulati in blagajniške prefekture, in sicer iz posamezne skupine le po ena služba. 4. Izvor legatov vzhodnih legij se sklada s splošnimi razvojnimi tendencami v sestavi rimskega senata. Že v prvi polovici 1. stoletja n. e. nastopajo nekateri homines novi iz Italije, proti koncu Neronove vlade prispeva prve provincialce Gallia Narbonensis in Hispania Baetica, prvi orijentalec se pojavi pod Flavijci, prvi Afrikanci pa okoli srede 2. stoletja. Od tedaj provincialci prevladujejo, vendar tudi še v 3. stoletju Italikov ne izpodrinejo povsem
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