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1.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
2.
Tetsutaro Shibata 《Journal d'Analyse Mathématique》2001,83(1):109-120
We consider the perturbed elliptic Sine-Gordon equation on an interval-u″t+γsinu(t)=μf(u(t)),t ∈I := (-T, T),u(t) > 0,t ∈I,u(±T)=0 where λ, μ>0 are parameters andT>0 is a constant. By applying variational methods subject to the constraint depending on λ, we obtain eigenpairs (μ,u)=(μ(λ),u
λ) which solve this eigenvalue problem for a given λ>0. Then we study the asymptotic behavior ofu
λ and μ(λ) as λ→∞. Especially, we study the location of interior transition layers ofu
λ as λ→∞.
This research has been supported by the Japan Society for the Promotion of Science. 相似文献
3.
Xiao-yu Xing Xue-qiang Wang 《应用数学学报(英文版)》2008,24(1):75-84
Consider a storage model fed by a Markov modulated Brownian motion. We prove that the stationary distribution of the model exits and that the running maximum of the storage process over the interval [0, t] grows asymptotically like log t as t→∞. 相似文献
4.
Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H
n
, n > 2. For ν > 0, the Brownian bridge B
(ν) of length ν on H is the process B
t
, 0 ≤t≤ν, conditioned by B
0 = B
ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge
on ℝ3). The same result holds for the simple random walk on an homogeneous tree.
Received: 4 December 1998 / Revised version: 22 January 1999 相似文献
5.
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion
started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and
the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional
Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this
Bessel bridge stays below some fixed value. 相似文献
6.
Alain Haraux 《Journal d'Analyse Mathématique》2005,95(1):297-321
IfA=A
*≥0 on the real Hilbert spaceH=L
2
(Ω, dμ) withKerA=A
−1
({0})∈0, (I+A)−1 compact andf(u)=c|u|
p−1
u withc>0,p>1, the solutions ofu”+u’+Au+f(u)=0 tend to 0 in norm at least liket
−1/(p−1)
ast→∞. Here it is shown that the set of initial data of those solutions tending to 0 exponentially fast has near 0 the structure
of a manifold with codimension dim(Ker A). If, in addition,A=−Δ with Neumann homogeneous boundary conditions, we show that the following alternative holds true: eitheru(t) tends to 0 exponentially fast, or ‖u(t)‖≥γt
−1/(p−1) with γ>0 fort≥1. 相似文献
7.
Sopra un principio di trasformazione integrale dei problemi differenziali ed alcune sue applicazioni
Guido Ascoli 《Annali di Matematica Pura ed Applicata》1955,40(1):167-182
Sunto Sviluppando ampiamente un'idea diWhittaker, si studiano trasformazioni del tipo
che mutano le soluzioni di una equazione differenziale lineareL
tx+λM
tx=0, appartenenti ad una classe lineare (G), opportunamente precisata, in soluzioni di una seconda equazione differenzialeP
uy+λQ
uy=0, appartenenti ad un'altra classe lineare (Γ). Il primo problema si suppone autoaggiunto. Il nucleo K è una soluzione dell'equazione
(L
t
Q
u −M
t
P
u)K=0, di classe (G) come funzione di t, di classe (Γ) come funzione di u. Il procedimento permette di stabilire proprietà
integrali in base a sole verifiche qualitative; ne vengono fatte applicazioni alle funzioni diMathieue diBessele ai polinomi diLegendree diHermite.
A Mauro Picone nel suo 70mo compleanno. 相似文献
8.
Youssef Randjiou 《Journal of Theoretical Probability》2006,19(3):701-720
Let μ+(t) and μ−(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ+(t) and μ−(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ+(t),μ−(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields
76, 477–497].
相似文献
9.
In this paper, the process {X(t); t>0}, representing the position of a uniformly accelerated particle (with Poisson-paced) changes of its acceleration, is studied.
It is shown that the distribution ofX(t) (suitably normalized), conditionally on the numbern of changes of acceleration, tends in distribution to a normal variate asn goes to infinity. The asymptotic normality of the unconditional distribution ofX(t) for large values oft is also shown. The study of these limiting distributions is motivated by the difficulty of evaluating exactly the conditional
and unconditional probability laws ofX(t). In fact, the results obtained in this paper permit us to give useful approximations of the probability distributions of
the position of the particle.
Dipartmento di Statistica, Probabilità Statistiche Applicate University of Rome “La Sapienza,” Italy. Published in Lietuvos
Matematikos Rinkinys, Vol. 37, No. 3, pp. 295–308, July–September, 1997. 相似文献
10.
If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ
u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when
g and G are taken to come from one of Laplace, logistic, Student’s t, uniform, exponential power or the Bessel function distribution.
相似文献
11.
L. Saloff-Coste 《Journal of Geometric Analysis》2004,14(4):715-733
Let M =G/H be an irreducible homogeneous compact manifold of dimension n equipped with its canonical Riemannian metric. Let γ be
the lowest nonzero eigenvalue of the Laplace operator. Let μ be the normalized Haar measure and μ
t be the heat diffusion measure, i.e., the law of Brownian motion started at a fixed origin in M. We show that the total variation
distance between μt and μ is not small for t ≪λ
−1 logn.This is sharp, up to a factor of two, in the case of compact irreducible simply connected symmetric spaces. 相似文献
12.
13.
Mario Abundo 《Methodology and Computing in Applied Probability》2010,12(3):473-490
It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion, driven by the stochastic differential
equation dX(t) = μ(X(t))dt + σ(X(t)) dB
t
, X(0) = x
0, through b + Y(t), where b > x
0 and Y(t) is a compound Poisson process with rate λ > 0 starting at 0, which is independent of the Brownian motion B
t
. In particular, the FPT density is investigated, generalizing a previous result, already known in the case when X(t) = μt + B
t
, for which the FPT density is the solution of a certain integral equation. A numerical method is shown to calculate approximately
the FPT density; some examples and numerical results are also reported. 相似文献
14.
Letu be a weak solution of the initial boundary value problem for the semilinear parabolic system of order 2m:u′(t)+Au(t)+f(t,.,u,..., ▽
m
u)=0. Letf satisfy controllable growth conditions. Thenu is smooth.
This result is proved by a kind of continuity method, where the timet is the parameter of continuity. 相似文献
15.
Pierre Collet Servet Martínez Jaime San Martín 《Probability Theory and Related Fields》2000,116(3):303-316
We study the asymptotic behaviour of the transition density of a Brownian motion in ?, killed at ∂?, where ?
c
is a compact non polar set. Our main result concern dimension d = 2, where we show that the transition density p
?
t
(x, y) behaves, for large t, as
u(x)u(y)(t(log t)2)−1 for x, y∈?, where u is the unique positive harmonic function vanishing on (∂?)
r
, such that u(x) ∼ log ∣x∣.
Received: 29 January 1999 / Revised version: 11 May 1999 相似文献
16.
If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ
u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when
g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.
相似文献
17.
M. Schmuckenschläger 《Potential Analysis》2011,35(3):287-300
This first result of this paper is about the Laplace transform of u(X
T
) where u is harmonic on some bounded domain Ω, X
t
is Brownian motion and T is the exit time from Ω. The following results focus on exit times from balls and Faber–Krahn and reverse Faber–Krahn type
inequalities for balls. We also study the behaviour of the first Dirichlet eigenvalue for complex balls under complex interpolation.
The method of proof heavily relays on the log-concavity of gaussian measures. 相似文献
18.
Tetsutaro Shibata 《Annali di Matematica Pura ed Applicata》2003,182(2):211-229
We consider the two-parameter nonlinear eigenvalue problem?−Δu = μu − λ(u + u
p
+ f(u)), u > 0 in Ω, u = 0 on ∂Ω,?where p>1 is a constant and μ,λ>0 are parameters. We establish the asymptotic formulas for the variational eigencurves λ=λ(μ,α) as
μ→∞, where α>0 is a normalizing parameter. We emphasize that the critical case from a viewpoint of the two-term asymptotics
of the eigencurve is p=3. Moreover, it is shown that p=5/3 is also a critical exponent from a view point of the three-term asymptotics when Ω is a ball or an annulus. This sort
of criticality for two-parameter problems seems to be new.
Received: February 9, 2002; in final form: April 3, 2002?Published online: April 14, 2003 相似文献
19.
Li Changpin 《应用数学学报(英文版)》2001,17(2):191-199
In this paper, we investigate the bifurcations of one class of steady-state reaction-diffusion equations of the formu″ + μu − u
k=0, subjectu(0)=u(π)=0, where μ is a parameter, 4≤kεZ
+. Using the singularity theory based on the Liapunov-Schmidt reduction, some satisfactory results are obtained.
This work is supported by the National Natural Science Foundation of China (No.19971057) and the Youth Science Foundation
of Shanghai Municipal Commission of Education (No.99QA66). 相似文献
20.
Zhu Ning 《高校应用数学学报(英文版)》1998,13(3):241-250
ANOTEONTHEBEHAVIOROFBLOW┐UPSOLUTIONSFORONE┐PHASESTEFANPROBLEMSZHUNINGAbstract.Inthispaper,thefolowingone-phaseStefanproblemis... 相似文献