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1.
Suppose (X,d) be a complete metric space, and suppose F:XCB(X) be a set-valued map satisfies H(Fx,Fy)≤ψ(d(x,y)), , where ψ:[0,)→[0,) is upper semicontinuous, ψ(t)<t for each t>0 and satisfies lim inft(tψ(t))>0. Then F has a unique endpoint if and only if F has the approximate endpoint property.  相似文献   

2.
Let (t∈[0,1]) be the indefinite Skorohod integral on the canonical probability space (Ω,F,P), and let Lt(x) (t∈[0,1], xR) be its the generalized local time introduced by Tudor in [C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli 10 (2004) 313-325]. We prove that the generalized local time, as function of x, has the same Besov regularity as the Brownian motion, as function of t, under some conditions imposed on the anticipating integrand u.  相似文献   

3.
Let (X,Y),(X1,Y1),(X2,Y2),… denote independent positive random vectors with common distribution function F(x,y)=P(X?x,Y?y) with F(x,y)<1 for all x,y. Based on the Xi and the Yj we construct the sum sequences and respectively. For a double sequence of weighting constants {b(n,m)} we associate a weighted renewal function G(x,y) defined as . The function G(x,y) can be expressed in terms of well-known renewal quantities. The main goal of this paper is to study asymptotic properties of G(x,y). In the one-dimensional case such results have been obtained among others by Omey and Teugels [Weighted renewal functions: a hierarchical approach, Adv. in Appl. Probab. 34 (2002) 394-415.] and Alsmeyer [Some relations between harmonic renewal measures and certain first passage times, Statist. Probab. Letters 12 (1991) 19-27; On generalized renewal measures and certain first passage times, Ann. Probab. 20 (1992) 1229-1247]. Here we prove a multivariate version of the elementary renewal theorem and moreover we obtain a rate of convergence result in this elementary renewal theorem. We close the paper with an application and some concluding remarks. For convenience we prove and formulate the results in the two-dimensional case only.  相似文献   

4.
5.
Let F=F(t,x) be a bounded, Hausdorff continuous multifunction with compact, totally disconnected values. Given any y0F(t0,x0), we show that the differential inclusion has a globally defined classical solution, with x(t0)=x0, .  相似文献   

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7.
Let x?s,t(x) be a -valued stochastic homeomorphic flow produced by non-Lipschitz stochastic differential equation , where W=(W1,W2,…) is an infinite sequence of independent standard Brownian motions. We first give some estimates of modulus of continuity of {?s,t(⋅)}, then prove that the flow ?s,t(x), when x nears infinity, grows slower than for some constant c>0 and integrable random variable Z via lemma of Garsia-Rodemich-Rumsey Lemma (abbreviated as GRR Lemma) improved by Arnold and Imkeller [L. Arnold, P. Imkeller, Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory, Stochastic Process. Appl. 62 (1996) 19-54] and moment estimates for one- and two-point motions.  相似文献   

8.
Let X be a normed linear space and be the unit sphere of X. Let , , and J(X)=sup{‖x+y‖∧‖xy‖}, x and yS(X) be the modulus of convexity, the modulus of smoothness, and the modulus of squareness of X, respectively. Let . In this paper we proved some sufficient conditions on δ(?), ρX(?), J(X), E(X), and , where the supremum is taken over all the weakly null sequence xn in X and all the elements x of X for the uniform normal structure.  相似文献   

9.
For a given set X, the set F(X) of all maps from X to X forms a semigroup under composition. A subsemigroup S of F(X) is said to be saturated if for each xX there exists a set OxX with xOx such that . It is shown that there exists a one-to-one correspondence between principal topologies on X and saturated subsemigroups of F(X). Some properties of principal topologies on X and the corresponding properties of their associated saturated subsemigroups of F(X) are discussed.  相似文献   

10.
Let X be a Green domain in Rd, d?2, xX, and let Mx(P(X)) denote the compact convex set of all representing measures for x. Recently it has been proven that the set of harmonic measures , U open in X, xU, which is contained in the set of extreme points of Mx(P(X)), is dense in Mx(P(X)). In this paper, it is shown that Mx(P(X)) is not a simplex (and hence not a Poulsen simplex). This is achieved by constructing open neighborhoods U0, U1, U2, U3 of x such that the harmonic measures are pairwise different and . In fact, these measures form a square with respect to a natural L2-structure. Since the construction is mainly based on having certain symmetries, it can be carried out just as well for Riesz potentials, the Heisenberg group (or any stratified Lie algebra), and the heat equation (or more general parabolic situations).  相似文献   

11.
12.
Gleason [A.M. Gleason, The definition of a quadratic form, Amer. Math. Monthly 73 (1966) 1049-1066] determined all functionals Q on K-vector spaces satisfying the parallelogram law Q(x+y)+Q(x-y)=2Q(x)+2Q(y) and the homogeneity Q(λx)=λ2Q(x). Associated with Q is a unique symmetric bi-additive form S such that Q(x)=S(x,x) and 4S(x,y)=Q(x+y)-Q(x-y). Homogeneity of Q corresponds to that of S: S(λx,λy)=λ2S(x,y). The associated S is not necessarily bi-linear.Let V be a vector space over a field K, char(K)≠2,3. A tri-additive form T on V is a map of V3 into K that is additive in each of its three variables. T is homogeneous of degree 3 if T(λx,λy,λz)=λ3T(x,y,z) for all .We determine the structure of tri-additive forms that are homogeneous of degree 3. One of the keys to this investigation is to find the general solution of the functional equation
F(t)+t3G(1/t)=0,  相似文献   

13.
If X is a real Banach space, we denote by WX the class of all functionals possessing the following property: if {un} is a sequence in X converging weakly to uX and lim infnΦ(un)≤Φ(u), then {un} has a subsequence converging strongly to u.In this paper, we prove the following result:Let X be a separable and reflexive real Banach space; an interval; a sequentially weakly lower semicontinuous C1 functional, belonging to WX, bounded on each bounded subset of X and whose derivative admits a continuous inverse on X; a C1 functional with compact derivative. Assume that, for each λI, the functional ΦλJ is coercive and has a strict local, not global minimum, say .Then, for each compact interval [a,b]⊆I for which , there exists r>0 with the following property: for every λ∈[a,b] and every C1 functional with compact derivative, there exists δ>0 such that, for each μ∈[0,δ], the equation
Φ(x)=λJ(x)+μΨ(x)  相似文献   

14.
Let N(X,B) be the number of rational points of height at most B on a variety XPn defined over Q. We establish new upper bounds for N(X,B) for hypersurfaces of dimension at most four. We also study N(X,B) for the open complements X of all lines or all planes on such hypersurfaces. One of the goals is to show that for smooth hypersurfaces in P5 defined by a form F(x0,…,x5) of degree d?9. This improves upon a classical upper estimate of Hua for the form .  相似文献   

15.
Let X be a complex Banach space and let I=(a,b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty(t)+αy(t)+βtrx0=0 for the class of continuously differentiable functions , where α, β and r are complex constants and x0 is an element of X. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.  相似文献   

16.
17.
Let X=(Xt)t?0 be a Lévy process and μ a positive Borel measure on R+. Suppose that the integral of μ defines a continuous increasing multifractal time . Under suitable assumptions on μ, we compute the singularity spectrum of the sample paths of the process X in time μ defined as the process (XF(t))t?0.A fundamental example consists in taking a measure μ equal to an “independent random cascade” and (independently of μ) a suitable stable Lévy process X. Then the associated process X in time μ is naturally related to the so-called fixed points of the smoothing transformation in interacting particles systems.Our results rely on recent heterogeneous ubiquity theorems.  相似文献   

18.
Let be the anticipating smooth semimartingale and be its generalized local time. In this paper, we give some estimates about the quasi sure property of Xt and its quadratic variation process tX〉. We also study the fractional smoothness of and prove that the quadratic variation process of can be constructed as the quasi sure limit of the form , where is a sequence of subdivisions of [a,b], , i=0,1,…,n2.  相似文献   

19.
Let u(t,x) be the solution of the heat equation (∂tx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞).  相似文献   

20.
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