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1.
A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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Ekaterina Vl. Bulinskaya 《Stochastic Processes and their Applications》2018,128(7):2325-2340
For a supercritical catalytic branching random walk on , , with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation. 相似文献
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In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type
in
, where Δp is the p-Laplacian operator, 1 < p < N, M:
and V:
are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik-Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation. 相似文献
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Romain Biard Bastien Mallein Landy Rabehasaina 《Stochastic Processes and their Applications》2018,128(7):2341-2366
We consider a branching random walk with values in a certain set , where the branching mechanism is different according to whether particles (individuals) are in a certain so called trapping set or not. We are then interested, under different scenarios, in properties of either the transient random measure describing distribution of individuals on over time or its asymptotic behaviour. 相似文献
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Christophe Cuny Jérôme Dedecker Florence Merlevède 《Stochastic Processes and their Applications》2018,128(4):1347-1385
The famous results of Komlós, Major and Tusnády (see Komlós et al., 1976 [15] and Major, 1976 [17]) state that it is possible to approximate almost surely the partial sums of size of i.i.d. centered random variables in () by a Wiener process with an error term of order . Very recently, Berkes et al. (2014) extended this famous result to partial sums associated with functions of an i.i.d. sequence, provided a condition on a functional dependence measure in is satisfied. In this paper, we adapt the method of Berkes, Liu and Wu to partial sums of functions of random iterates. Taking advantage of the Markovian setting, we shall give new dependent conditions, expressed in terms of a natural coupling (in or in ), under which the strong approximation result holds with rate . As we shall see our conditions are well adapted to a large variety of models, including left random walks on , contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains. We also provide some examples showing that our -coupling condition is in some sense optimal. 相似文献
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Gianfranco Casnati Daniele Faenzi Francesco Malaspina 《Journal of Pure and Applied Algebra》2018,222(3):585-609
In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3. 相似文献
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赵晓军 《数学物理学报(B辑英文版)》2018,38(2):673-680
In this article, we study the nonexistence of solution with finite Morse index for the following Choquard type equation-△u=∫RN|u(y)|p|x-y|αdy|u(x)|p-2u(x) in RN where N ≥ 3, 0 α min{4, N}. Suppose that 2 p (2 N-α)/(N-2),we will show that this problem does not possess nontrivial solution with finite Morse index. While for p=(2 N-α)/(N-2),if i(u) ∞, then we have ∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~α dxdy ∞ and ∫_RN|▽u|~2 dx=∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~αdxdy. 相似文献
11.
Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
12.
Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion on and the slit motion . The diffusion coefficient and drift coefficient of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as . We introduce a function measuring the discrepancy of a standard slit domain from relative to BMD. We show that enjoys a locality property. 相似文献
14.
Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
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Let be a purely discontinuous additive functional of a subordinate Brownian motion . We give a sufficient condition on the non-negative function that guarantees that finiteness of implies finiteness of its expectation. This result is then applied to study the relative entropy of and the probability measure induced by a purely discontinuous Girsanov transform of the process . We prove these results under the weak global scaling condition on the Laplace exponent of the underlying subordinator. 相似文献
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Ozhan Genc 《Journal of Pure and Applied Algebra》2018,222(1):213-240
In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of , Q (smooth quadric in ), (smooth cubic in ) or (complete intersection of two quadrics in ) along a smooth irreducible curve. We prove that the only class which admits Ulrich line bundles is the one obtained by blowing up a genus 3, degree 6 curve in . Also, we prove that there exist stable rank two Ulrich bundles with on a generic member of this deformation class. 相似文献
20.
D. Buraczewski E. Damek J. Zienkiewicz 《Stochastic Processes and their Applications》2018,128(9):2923-2951
We consider first passage times for the perpetuity sequence where are i.i.d. random variables with values in . Recently, a number of limit theorems related to were proved including the law of large numbers, the central limit theorem and large deviations theorems (see Buraczewski et al., in press). We obtain a precise asymptotics of the sequence , , which considerably improves the previous results of Buraczewski et al. (in press). There, probabilities were identified, for some large intervals around , with lengths growing at least as . Remarkable analogies and differences to random walks (Buraczewski and Ma?lanka, in press; Lalley, 1984) are discussed. 相似文献