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1.
We estimate a median of f(Xt) where f is a Lipschitz function, X is a Lévy process and t is an arbitrary time. This leads to concentration inequalities for f(Xt). In turn, corresponding fluctuation estimates are obtained under assumptions typically satisfied if the process has a regular behavior in small time and a, possibly different, regular behavior in large time. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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For certain Gaussian processes X(t) with trend −ctβ and variance V2(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t)−ctβ≥u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u→∞ showing that the limiting distribution depends on the parameters β, V(t) and the correlation function of X(t). 相似文献
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Let (X,d) be a metric space endowed with a graph G such that the set V(G) of vertices of G coincides with X. We define the notion of G-Reich type maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on ordered metric spaces and for cyclic operators. 相似文献
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Let G be a connected regular graph. Denoted by t(G) and Kf(G) the total graph and Kirchhoff index of G, respectively. This paper is to point out that Theorem 3.7 and Corollary 3.8 from “Kirchhoff index in line, subdivision and total graphs of a regular graph” [X. Gao, Y.F. Luo, W.W. Liu, Kirchhoff index in line, subdivision and total graphs of a regular graph, Discrete Appl. Math. 160(2012) 560–565] are incorrect, since the conclusion of a lemma is essentially wrong. Moreover, we first show the Laplacian characteristic polynomial of t(G), where G is a regular graph. Consequently, by using Kf(G), we give an expression on Kf(t(G)) and a lower bound on Kf(t(G)) of a regular graph G, which correct Theorem 3.7 and Corollary 3.8 in Gao et al. (2012) [2]. 相似文献
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(Xt,α) and diffusion coefficient εa(Xt,β) where α and β are two unknown parameters, while ε is known. For a high frequency sample of observations of the diffusion at the time points k/n, k=1,…,n, we propose a class of contrast functions and thus obtain estimators of (α,β). The estimators are shown to be consistent and asymptotically normal when n→∞ and ε→0 in such a way that ε−1n−ρ remains bounded for some ρ>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function. 相似文献
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Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We show that all subsequential limits of this ratio at 0 (∞) are continuous for any nondegenerate F with finite expectation if and only if Vt belongs to the centered Feller class at 0 (∞). We also characterize when Ut/Vt has a non-degenerate limit distribution at 0 and ∞. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models (X,V) where both the state process X and the volatility process V may have jumps. Our results relate the asymptotic behavior of the characteristic function of XΔ for some Δ>0 in a stationary regime to the Blumenthal–Getoor indexes of the Lévy processes driving the jumps in X and V. The results obtained are used to construct consistent estimators for the above Blumenthal–Getoor indexes based on low-frequency observations of the state process X. We derive convergence rates for the corresponding estimator and show that these rates cannot be improved in general. 相似文献
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In this article, we consider a jump diffusion process (Xt)t≥0 observed at discrete times t=0,Δ,…,nΔ. The sampling interval Δ tends to 0 and nΔ tends to infinity. We assume that (Xt)t≥0 is ergodic, strictly stationary and exponentially β-mixing. We use a penalised least-square approach to compute two adaptive estimators of the drift function b. We provide bounds for the risks of the two estimators. 相似文献
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A d-arc-dominated digraph is a digraph D of minimum out-degree d such that for every arc (x,y) of D, there exists a vertex u of D of out-degree d such that (u,x) and (u,y) are arcs of D. Henning and Yeo [Vertex disjoint cycles of different length in digraphs, SIAM J. Discrete Math. 26 (2012) 687–694] conjectured that a digraph with minimum out-degree at least four contains two vertex-disjoint cycles of different length. In this paper, we verify this conjecture for 4-arc-dominated digraphs. 相似文献
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We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
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For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in law with a correction term which is an Itô integral of f? with respect to a Gaussian martingale independent of X. The proof uses Malliavin calculus and a central limit theorem from Nourdin and Nualart (2010) [8]. This formula was known for fBm with H=1/6 Nourdin et al. (2010) [9]. We extend this to a larger class of Gaussian processes. 相似文献
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Brooks’ theorem is a fundamental result in the theory of graph coloring. Catlin proved the following strengthening of Brooks’ theorem: Let d be an integer at least 3, and let G be a graph with maximum degree d. If G does not contain Kd+1 as a subgraph, then G has a d-coloring in which one color class has size α(G). Here α(G) denotes the independence number of G. We give a unified proof of Brooks’ theorem and Catlin’s theorem. 相似文献
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Let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge, and Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. In this paper, we determine the Laplacian polynomials of R(G) and Q(G) of a regular graph G; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. 相似文献