共查询到20条相似文献,搜索用时 203 毫秒
1.
2.
LetX be a strongly symmetric standard Markov process on a locally compact metric spaceS with 1-potential densityu
1(x, y). Let {L
t
y
, (t, y)R
+×S} denote the local times ofX and letG={G(y), yS} be a mean zero Gaussian process with covarianceu
1(x, y). In this paper results about the moduli of continuity ofG are carried over to give similar moduli of continuity results aboutL
t
y
considered as a function ofy. Several examples are given with particular attention paid to symmetric Lévy processes.The research of both authors was supported in part by a grant from the National Science Foundation. In addition the research of Professor Rosen was also supported in part by a PSC-CUNY research grant. Professor Rosen would like to thank the Israel Institute of Technology, where he spent the academic year 1989–90 and was supported, in part, by the United States-Israel Binational Science Foundation. Professor Marcus was a faculty member at Texas A&M University while some of this research was carried out. 相似文献
3.
P. J. Brockwell 《Annals of the Institute of Statistical Mathematics》2001,53(1):113-124
Properties and examples of continuous-time ARMA (CARMA) processes driven by Lévy processes are examined. By allowing Lévy processes to replace Brownian motion in the definition of a Gaussian CARMA process, we obtain a much richer class of possibly heavy-tailed continuous-time stationary processes with many potential applications in finance, where such heavy tails are frequently observed in practice. If the Lévy process has finite second moments, the correlation structure of the CARMA process is the same as that of a corresponding Gaussian CARMA process. In this paper we make use of the properties of general Lévy processes to investigate CARMA processes driven by Lévy processes {W(t)} without the restriction to finite second moments. We assume only that W (1) has finite r-th absolute moment for some strictly positive r. The processes so obtained include CARMA processes with marginal symmetric stable distributions. 相似文献
4.
Václav Tryhuk 《Czechoslovak Mathematical Journal》2000,50(3):499-508
The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form
f( t,uy,wy + uuz ) = f( x,y,z )u2 u+ g( t,x,u,u,w )uz + h( t,x,u,u,w )y + 2uwzf\left( {t,\upsilon y,wy + u\upsilon z} \right) = f\left( {x,y,z} \right)u^2 \upsilon + g\left( {t,x,u,\upsilon ,w} \right)\upsilon z + h\left( {t,x,u,\upsilon ,w} \right)y + 2uwz 相似文献
5.
Let X={X(t):tR} be a Lévy process and a non-decreasing, right continuous, bounded function with (–)=0 (((1+u
2)/u
2)d(u) is the Lévy measure). In this paper we define the Donsker delta function (X(t)–a), t>0 and aR, as a generalized Lévy functional under the condition that (0)–(0–)>0. This leads us to define F(X(t)) for any tempered distribution F, and as an application, we derive an Itô formula for F(X(t)) when has jumps at 0 and 1. 相似文献
6.
Qi-kang Ran Ai-nong FangDepartment of Applied Mathematics Shanghai University of Finance Economics Shanghai ChinaDepartment of Applied Mathematics Shanghai Jiaotong University Shanghai China 《应用数学学报(英文版)》2002,18(3):461-470
In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p. 相似文献
7.
In-Suk Wee 《Probability Theory and Related Fields》1992,93(3):359-376
Summary Let {X
t
} be a one-dimensional Lévy process with local timeL(t, x) andL
*(t)=sup{L(t, x): x }. Under an assumption which is more general than being a symmetric stable process with index >1, we obtain a LIL forL*(t). Also with an additional condition of symmetry, a LIL for range is proved.This research is supported by a grant from Korea Science and Engineering Foundations 相似文献
8.
Jürgen Weyer 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1983,34(5):728-745
Summary We study positive solutions of the nonlinear eigenvalue problemF(u)=G(u) with some monotone operatorsF andG. In particular, we consider the case of nonlinear elliptic differential equations of second order and chooseF(u)=–divA(x, gradu)+b(x,u) and G(u)=g (x,u). Positive solutions are obtained by the Picard iterationsu
0=0 andF(u
n+1)=G(u
n
).In order to get convergence of the sequenceu
n
,one has to study some comparison principles for the operatorF. Finally, the Picard iteration scheme allows a-priori estimates and bifurcation results for the admissible eigenvalue parameter.
Zusammenfassung Für gewisse monotone OperatorenF andG untersuchen wir positive Lösungen des nichtlinearen EigenwertproblemsF(u)=G(u). Insbesondere betrachten wir nichtlineare elliptische Differentialgleichungen zweiter Ordnung und wählenF(u)=–divA(x, gradu)+b(x,u) sowieG(u)=g(x,u). Man erhält positive Lösungen durch das Picard-Iterationsverfahrenu 0=0 undF(u n+1)=G(u n ).Um die Konvergenz der Folgeu n nachzuweisen, benötigt man Vergleichsprinzipien fürF. Dann gestattet das Iterationsschema sogar a-priori Abschätzungen und Verzweigungsaussagen für die zulässigen Eigenwertparameter. Supported by the Deutscher Akademischer Austauschdienst (DAAD) and DICYT-University of Santiago de Chile. 相似文献 9.
Let (
t
)
t>0 be a symmetric weakly continuous semigroup of probability measures on a nonabelien complete separable group G and let v be its Lévy measure. The purpose of this paper is to provide a relatively simple proof of the zero-one law for semigroups with the Lévy measure satisfying either v(H
c) = or v(H
c) = 0. 相似文献
10.
S. Haruki 《Aequationes Mathematicae》2002,63(3):201-209
Summary. Let (G, +) and (H, +) be abelian groups such that the equation 2u = v 2u = v is solvable in both G and H. It is shown that if f1, f2, f3, f4, : G ×G ? H f_1, f_2, f_3, f_4, : G \times G \longrightarrow H satisfy the functional equation f1(x + t, y + s) + f2(x - t, y - s) = f3(x + s, y - t) + f4(x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , then f1, f2, f3, and f4 are given by f1 = w + h, f2 = w - h, f3 = w + k, f4 = w - k where w : G ×G ? H w : G \times G \longrightarrow H is an arbitrary solution of f (x + t, y + s) + f (x - t, y - s) = f (x + s, y - t) + f (x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , and h, k : G ×G ? H h, k : G \times G \longrightarrow H are arbitrary solutions of Dy,t3g(x,y) = 0 \Delta_{y,t}^{3}g(x,y) = 0 and Dx,t3g(x,y) = 0 \Delta_{x,t}^{3}g(x,y) = 0 for all x, y, s, t ? G x, y, s, t \in G . 相似文献
11.
Quasilinear elliptic equations with boundary blow-up 总被引:2,自引:0,他引:2
Jerk Matero 《Journal d'Analyse Mathématique》1996,69(1):229-247
Assume that Ω is a bounded domain in ℝ
N
withN ≥2, which has aC
2-boundary. We show that forp ∃ (1, ∞) there exists a weak solutionu of the problem δp
u(x) = f(u(x)), x ∃ Ω with boundary blow-up, wheref is a positive, increasing function which meets some natural conditions. The boundary blow-up ofu(x) is characterized in terms of the distance ofx from ∂Ω. For the Laplace operator, our results coincide with those of Bandle and Essén [1]. Finally, for a rather wide subclass
of the class of the admissible functionsf, the solution is unique whenp ∃ (1, 2]. 相似文献
12.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
13.
Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, U the right Utumi quotient ring of R, f(x 1,…, x n ) a noncentral multilinear polynomial over K, and G a nonzero generalized derivation of R. Denote f(R) the set of all evaluations of the polynomial f(x 1,…, x n ) in R. If [G(u)u, G(v)v] = 0, for any u, v ∈ f(R), we prove that there exists c ∈ U such that G(x) = cx, for all x ∈ R and one of the following holds: 1. f(x 1,…, x n )2 is central valued on R; 2. R satisfies s 4, the standard identity of degree 4. 相似文献
14.
This paper presents a systematic study of the class of multivariate distributions obtained by a Gaussian randomization of jumps of a Lévy process. This class, called the class of type G distributions, constitutes a closed convolution semigroup of the family of symmetric infinitely divisible probability measures. Spectral form of Lévy measures of type G distributions is obtained and it is shown that type G property can not be determined by one dimensional projections. Conditionally Gaussian structure of type G random vectors is exhibited via series representations. 相似文献
15.
T. E. Pyasetskaya 《Journal of Mathematical Sciences》1993,67(4):3225-3228
We consider the behavior of a solution of the wave equation utt (t, x) – a2 (t) uxx (t, x)=f (t, x) with initial conditions u (0, x)=u0, /t6t u (t, x) ¦t=0
=u1 (x), a andf being random functions; a(t) characteristizes the variable character of the medium;f(t, x) is the inhomogeneity, having the character of random walks.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 75–78, 1988. 相似文献
16.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献
17.
We prove Harnacks inequality for harmonic functions of a symmetric stable Lévy process on Rd without the assumption that the density function of its Lévy measure is locally bounded from below.
Mathematics Subject Classifications (2000) Primary 60J45, 31C05; Secondary 60G51.Research partially supported by KBN (2P03A 041 22) and RTN (HPRN-CT-2001-00273-HARP). 相似文献
18.
We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy
Laplacian ∆
L
resolved with respect to the derivative
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