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作者：Dawson, DA; Fleischmann, K; Leduc, G
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Quebec; University of Quebec Montreal
摘要：A general class of finite variance critical (xi, Phi, k)-superprocesses X in a Luzin space E with cadlag right Markov motion process xi, regular local branching mechanism Phi and branching functional k of bounded characteristic are shown to continuously depend on (Phi, k). As an application we show that the processes with a classical branching functional k(ds) = rho(s)(xi(s))ds [that is, a branching functional k generated by a classical branching rate rho(s)(gamma)] are dense in the above clas...
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作者：Uchiyama, K
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：It is shown that an infinite subset of Z(N) is either recurrent for each aperiodic N-dimensional random walk with mean zero and finite variance, or transient for each of such random walks. This is an exact extension of the result by Spitzer in three dimensions to that in the dimensions N greater than or equal to 4.
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作者：Le Gall, JF; Le Jan, Y
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism. This construction depends on a path-valued process called the Levy snake, which is of independent interest. Our method of proof involves a calculation of the Laplace functional of the occupation field of the Levy snake. This calculation relies on an evaluation of the corresponding moment functionals, which requires precise information about the underl...
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作者：Hahn, MG; Klass, MJ
作者单位：Tufts University; University of California System; University of California Berkeley
摘要：This paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary lid. random variables. The introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary lid. random variables. More specifically, let n be a fixed natural number and let Z, Z(1), Z(2),..., Z(n) be arbitrary i.i.d. random variables We construct a function F-Z,F- n(a), derived from the probabi...
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作者：Lifshits, MA
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：The behavior of tail probabilities P{S less than or equal to r}, r --> 0 is investigated, where S is a series S = Sigma lambda(j)Z(j) generated by some sequence of positive numbers {lambda(j)} and by a sequence {Z(j)} of independent copies of a positive random variable Z. We present the exact asymptotic expression for P{S less than or equal to r} by means of Laplace transform Lambda(gamma) = E exp{-gamma S} under weak assumptions on the behavior of the tail probabilities of Z in the vicinity o...
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作者：Sudbury, A; Lloyd, P
作者单位：Monash University; Monash University
摘要：Duality has proved to be a powerful technique in the study of interacting particle systems (IPS). This concept can be enlarged and a quasi-duality defined between various pairs of IPS previously thought unrelated. Consequently, theorems of a similar style to those involving duality can be deduced. The concept of quasi-duality follows naturally from our previous studies into the use of single-site operators (an idea borrowed from quantum physics) in paper II of this series. It is shown that a n...
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作者：Carmona, P
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Brownian motion in a random Levy potential V is the informal solution of the stochastic differential equation dX(t) = dB(t) - 1/2V' (X-t) dt, where B is a Brownian motion independent of V. We generalize some results of Kawazu-Tanaka, who considered for V a Brownian motion with drift, by proving that X-t/t converges almost surely to a constant, the mean velocity, which we compute in terms of the Levy exponent phi of V, defined by E[e(mV(t))] = e(-t phi(m)).
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作者：Deheuvels, P
作者单位：Sorbonne Universite
摘要：We show that increments of size h(n) from the uniform quantile and uniform empirical processes in the neighborhood of a fixed point t(0) is an element of (0, 1) may have different rates of almost sure convergence to 0 in the range where h(n) --> 0 and nh(n)/log n --> infinity. In particular, when h(n) + n(-lambda) with 0 < lambda < 1, we obtain that these rates are identical for 1/2 < lambda < 1, and distinct for 0 < lambda < 1/2. This phenomenon is shown to be a consequence of functional laws...
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作者：Ben Arous, G; Guionnet, A
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the averaged law of the empirical measure on the path space of these dynamics satisfies a large deviation upper bound in the high temperature regime. We study the rate function which governs this large deviation upper bound and prove that it achieves its minimum value at a unique probability measure Q which is not Markovian: We deduce an ave...
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作者：van den Berg, J
作者单位：Centrum Wiskunde & Informatica (CWI)
摘要：For spin systems with random, finite-range interactions, we define an analog of the usual weak mixing property, which we call weak mixing in expectation (WME). This property implies (almost sure) uniqueness of the Gibbs measure. We concentrate on the two-dimensional case, for which we present finite-volume conditions which are sufficient for WME. We also show the reverse: if the system is WME, then the condition is satisfied for some (sufficiently large) volume. Simultaneously, we obtain an ex...
