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1.
Consider a central Gaussian convolution semigroup (μ
t
)
t > 0
on a connected compact semisimple group. Then either the measure μ
t
is singular with respect to Haar measure for all t > 0, or there exists a time t such that μ
t
is absolutely continuous with respect to Haar measure and admits a continuous density.
Received: 6 November 2001 / Revised version: 13 June 2002 / Published online: 30 September 2002
Research partially supported by NSF grant DMS 0102126
Mathematics Subject Classification (2000): 28C10, 28C20, 60B15, 60G30
Keywords or phrases: Gaussian convolution semigroups – Dichotomy – Absolute continuity 相似文献
2.
We will study the following problem.Let X_t,t∈[0,T],be an R~d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σcontaining an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation. 相似文献
3.
We study the persistence of the asymptotic stability of delay equations both under linear and nonlinear perturbations. Namely,
we consider nonautonomous linear delay equations v′ = L(t)v
t
with a nonuniform exponential contraction. Our main objective is to establish the persistence of the nonuniform exponential stability of the
zero solution both under nonautonomous linear perturbations, i.e., for the equation v′ = (L(t) + M(t))v
t
, thus discussing the so-called robustness problem, and under a large class of nonlinear perturbations, namely for the equation
v′ = L(t)v
t
+ f(t, v
t
). In addition, we consider general contractions e
−λρ(t) determined by an increasing function ρ that includes the usual exponential behavior with ρ(t) = t as a very special case. We also obtain corresponding results in the case of discrete time. 相似文献
4.
Subordination of a killed Brownian motion in a bounded domain D⊂ℝ
d
via an α/2-stable subordinator gives a process Z
t
whose infinitesimal generator is −(−Δ|
D
)α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process Z
t
in a Lipschitz domain D by comparing the process with the rotationally invariant α-stable process killed upon exiting D. We show that these processes have comparable killing measures, prove the intrinsic ultracontractivity of the generator of
Z
t
, prove the intrinsic ultracontractivity of the semigroup of Z
t
, and, in the case when D is a bounded C
1,1
domain, obtain bounds on the Green function and the jumping kernel of Z
t
.
Received: 4 April 2002 / Revised version: 1 July 2002 / Published online: 19 December 2002
This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut
Oberwolfach. We thank the Institute for the hospitality.
The research of the first author is supported in part by NSF Grant DMS-9803240.
The research of the second author is supported in part by MZT grant 037008 of the Republic of Croatia.
Mathematics Subject Classification (2000): Primary 60J45; Secondary 60J75, 31C25
Key words or phrases: Killed Brownian motions – Stable processes – Subordination – Fractional Laplacian 相似文献
5.
Simone Borghesi 《Inventiones Mathematicae》2003,151(2):381-413
For any prime q and positive integer t, we construct a spectrum k(t) in the stable homotopy category of schemes over a field k equipped with an embedding k↪ℂ. In classical homotopy theory, the ℂ realization of k(t) is known as Morava K-theory. The algebraic content lies in the fact that these spectra are defined as the homotopy limit
of a tower whose cofibers are appropriate suspensions of the motivic Eilenberg-MacLane spectra, which are known to represent
motivic cohomology in the stable homotopy category of schemes.
Oblatum 26-XI-2001 & 5-VIII-2002?Published online: 8 November 2002 相似文献
6.
ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLICWAVES 总被引:1,自引:0,他引:1
YANG Han 《数学年刊B辑(英文版)》2000,21(1):63-70
Introduction1.1.ConsiderthefollowingquasilinearhyperbolicCauchyproblemwithlineardamping{:;;!OTt=-:i<:,;>>L06,(11)wherexER",t20,anda(.)isasmoothfunctionsatisfyinga(y)~1 O(lyl")aslyl-0,orEN.(1.2)Thepurposeofthispaperistoshowthat,atleastwhenn53,theasymptoticprofileofthesolutionu(x,t)of(l.1)isgivenbythesolutionv(x,t)ofthecorrespondingparabolicproblem{:;.t>ivj:相似文献
7.
8.
Werner Georg Nowak 《Monatshefte für Mathematik》2002,137(3):227-238
This article is concerned with sums 𝒮(t) = ∑
n
ψ(tf(n/t)) where ψ denotes, essentially, the fractional part minus ?, f is a C
4-function with f″ ≠ 0 throughout, summation being extended over an interval of order t. We establish an asymptotic formula for ∫
T−Λ
T+Λ
(𝒮(t))2dt for any Λ = Λ(T) growing faster than log T.
Received April 30, 2001; in revised form February 15, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
9.
N. G. Khoma 《Ukrainian Mathematical Journal》1998,50(12):1917-1923
In three spaces, we find exact classical solutions of the boundary-value periodic problem utt - a2uxx = g(x, t) u(0, t) = u(π, t) = 0, u(x, t + T) = u(x, t), x ∈ ℝ, t ∈ ℝ. We study the periodic boundary-value problem for a quasilinear equation whose left-hand side is the d’Alembert operator
and whose right-hand side is a nonlinear operator.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1680–1685, December, 1998. 相似文献
10.
G. P. Pelyukh 《Differential Equations》2012,48(4):609-613
We obtain conditions for the existence of continuous (for t ≥ T > 0) solutions for a wide class of systems of nonlinear difference equations with continuous argument and analyze their properties as t → +∞. 相似文献
11.
Alexander G. Ramm Alexandra B. Smirnova Angelo Favini 《Annali di Matematica Pura ed Applicata》2003,182(1):37-52
A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with
the trajectory starting at some initial point x
0 and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated.
Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003
This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks
DAAD for support 相似文献
12.
Philippe Souplet 《Annali di Matematica Pura ed Applicata》2002,181(4):427-436
We prove an a priori estimate and a universal bound for any global solution of the nonlinear degenerate reaction-diffusion
equation u
t
=Δu
m
+u
p
in a bounded domain with zero Dirichlet boundary conditions.
Received: October 1, 2001?Published online: July 9, 2002 相似文献
13.
H. Brézis 《Israel Journal of Mathematics》1971,9(4):513-534
Let φ be a convex l.s.c. function fromH (Hilbert) into ] - ∞, ∞ ] andD(φ)={u ∈H; φ(u)<+∞}. It is proved that for everyu
0 ∈D(φ) the equation − (du/dt)(t ∈ ∂φ(u(t)),u(0)=u
0 has a solution satisfying ÷(du(t)/dt)÷ ≦(c
1/t)+c
2. The behavior ofu(t) in the neighborhood oft=0 andt=+∞ as well as the inhomogeneous equation (du(t)/dt)+∂φ(u(t)) ∈f(t) are then studied. Solutions of some nonlinear boundary value problems are given as applications.
相似文献
14.
Antonio Tineo 《Annali di Matematica Pura ed Applicata》2003,182(2):129-141
In this paper we study the scalar equation x′=f(t,x), where f(t,x) has cubic non-linearities in x and we prove that this equation has at most three bounded separate solutions. We say that λ∈ℝ is a critical value of the
equation x′=f(t,x)+λx if this equation has a degenerate bounded solution and we exhibit two classes of functions f such that the above equation has a unique critical value.
Received: February 4, 2000; in final form: March 19, 2002?Published online: April 14, 2003
RID="*"
ID="*"This paper was partially supported by CDCHT, Universidad de los Andes. 相似文献
15.
16.
We construct small solutions x(t) → 0 as t → 0 of nonlinear operator equations F(x(t), x(α(t)),t) = 0 with a functional perturbation α(t) of the argument. By the Newton diagram method, we reduce the problem to quasilinear operator equations with a functional
perturbation of the argument. We show that the solutions of such equations can have not only algebraic but also logarithmic
branching points and contain free parameters. The number of free parameters and the form of the solution depend on the properties
of the Jordan structure of the operator coefficients of the equation. 相似文献
17.
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential
equation ẍ + g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)x
γ + b(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded.
This project was supported by the Program for New Century Excellent Talents of Ministry of Education of China and the National
Natural Science Foundation of China (Grant No. 10671020 and 10301006). 相似文献
18.
Analysis of a Free Boundary Problem Modeling Tumor Growth 总被引:4,自引:0,他引:4
Shang Bin CUI 《数学学报(英文版)》2005,21(5):1071-1082
In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions: R = R(t), the radius of the tumor, and u = u(r, t), the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 〈 r 〈 R(t), t 〉 0, and the function R satisfies a nonlinear integrodifferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t →∞. 相似文献
19.
The Ulm method is considered to approximate a solution of a nonlinear operator equation F(x) = 0. We study the convergence of this method when F′ is ω-conditioned and prove that the R-order of convergence is at least 1 + p if ω is quasi-homogeneous of type ω(tz)≤ t
p
ω(z), for z > 0, tϵ[0,1] and pϵ[0,1].
Preparation of this paper was partly supported by the Ministry of Education and Science (MTM 2005-03091). 相似文献
20.
Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension 总被引:5,自引:0,他引:5
Mu-Tao Wang 《Inventiones Mathematicae》2002,148(3):525-543
Let f:Σ1↦Σ2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of
f in Σ1×Σ2 by the mean curvature flow. Under suitable conditions on the curvature of Σ1 and Σ2 and the differential of the initial map, we show that the flow exists smoothly for all time. At each instant t, the flow remains the graph of a map f
t
and f
t
converges to a constant map as t approaches infinity. This also provides a regularity estimate for Lipschitz initial data.
Oblatum 30-I-2001 & 24-X-2001?Published online: 1 February 2002 相似文献