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1.
We derive characterizations for the Schur stability and the stability of all convex combinations of kk≥2, given real square matrices. Moreover, we characterize these properties for the set r(A, B) (c(A,B), resp.) of square matrices whose rows (columns, resp.) are independent convex combinations of the rows (columns, resp.) of two real matrices A and B. Our results can be viewed as contributions to the problem of robustness of matrix properties. This paper continues our paper [4]. 相似文献
2.
This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional random measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems. 相似文献
3.
Log-fractional stable processes 总被引:1,自引:0,他引:1
Yuji Kasahara 《Stochastic Processes and their Applications》1988,30(2):329-339
The first problem attacked in this paper is answering the question whether all 1/-self-similar -stable processes with stationary increments are -stable motions. The answer is yes for = 2, no for 1<2 and unknown for 0<<1. We single out the log-fractional stable processes for 1<2, different from -stable motions for ≠2. They can be regarded as the limit of fractional stable processes as the exponent in the kernel tends to 0. The paper ends with a limit theorem for partial sum processes of moving averages of iid random variables in the domain of attraction of a strictly stable law, with log-fractional stable processes as limits in law. The conditions involve de Haan's class Π of slowly varying functions. 相似文献
4.
A tempered stable Lévy process combines both the α-stable and Gaussian trends. In a short time frame it is close to an α-stable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization. We prove short and long time behavior of tempered stable Lévy processes and investigate their absolute continuity with respect to the underlying α-stable processes. We find probabilistic representations of tempered stable processes which specifically show how such processes are obtained by cutting (tempering) jumps of stable processes. These representations exhibit α-stable and Gaussian tendencies in tempered stable processes and thus give probabilistic intuition for their study. Such representations can also be used for simulation. We also develop the corresponding representations for Ornstein–Uhlenbeck-type processes. 相似文献
5.
We present several constructions of a ``censored stable process' in an open set DRn, i.e., a symmetric stable process which is not allowed to jump outside D.
We address the question of whether the process will approach the boundary of D in a finite time – we give sharp conditions for such approach in terms of the stability index and the ``thickness' of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent case.
We also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary. We derive a boundary Harnack principle in C1,1 open sets.
Research partially supported by NSF Grant DMS-0071486.Mathematics Subject Classification (2000): Primary 60G52, Secondary 60G17, 60J45 相似文献
6.
Yuzo Hosoya 《Probability Theory and Related Fields》1982,60(4):517-533
Summary This paper examines properties of a class of complex-valued stable processes which have spectral representation by means of independent-increments processes. A representation is derived by an application of Schilder's stochastic integral. Also, another construction of harmonizable stable processes by means of generalized stochastic processes is given, and its relation to the stochastic integral is shown. Some limit theorems of the Fourier transform of a sample from harmonizable stable processes are provided. Moreover, a linear prediction theory which pertains to those processes is suggested as an extension of that of second-order stationary processes. 相似文献
7.
Jean Bertoin 《Journal of Theoretical Probability》1994,7(3):551-563
One says thatt>0 is an increase time for a real-valued path if stays above the level (t) immediately after timet, and below (t) immediately before timet. Dvoretzkyet al.,(10) proved that Brownian motion has no increase times a.s. This result is extended here to (strictly) stable processes. Specifically, the probability that a stable processX possesses increase times is 0 if and only ifP(X
10)1/2. 相似文献
8.
We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes. 相似文献
9.
Zhen-Qing Chen 《Journal of Applied Mathematics and Computing》1999,6(2):227-266
This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions, Poisson kernels and Martin kernels of discontinuous symmetric α-stable process in boundedC 1,1 open sets. The new results give explicit information on how the comparing constants depend on parameter α and consequently recover the Green function and Poisson kernel estimates for Brownian motion by passing α ↑ 2. In addition to these new estimates, this paper surveys recent progress in the study of notions of harmonicity, integral representation of harmonic functions, boundary Harnack inequality, conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.
- Introduction
- Green function and Poisson kernel estimates
- Estimates on balls
- Estimates on boundedC 1,1 domains
- Estimates on boundedC 1,1 open sets
- Harmonic functions and integral representation
- Two notions of harmonicity
- Martin kernel and Martin boundary
- Integral representation and uniqueness
- Boundary Harnack principle
- Conditional process and its limiting behavior
- Conditional gauge and intrinsic ultracontractivity
10.
This paper deals with a characterization of a multivariate stable process using an independence property with a positive random variable. Moreover, we establish a characterization of a multivariate Lévy process based on the notion of cut in a natural exponential family. This allows us to draw some related properties. More precisely, we give the probability density function of this process and the law of the mixture of the Lévy process governed by the convolution semigroup with respect to an exponential random variable. These results are confidentially connected with the univariate case given by [G. Letac and V. Seshadri, Exponential stopping and drifted stable processes, Stat. Probab. Lett., 72:137–143, 2005]. 相似文献
11.
12.
Modelling financial and insurance time series with Lévy processes or with exponential Lévy processes is a relevant actual practice and an active area of research. It allows qualitatively and quantitatively good adaptation to the empirical statistical properties of asset returns. Due to model incompleteness it is a problem of considerable interest to determine the dependence of option prices in these models on the choice of pricing measures and to establish nontrivial price bounds. In this paper we review and extend ordering results of stochastic and convex type for this class of models. We also extend the ordering results to processes with independent increments (PII) and present several examples and applications as to α-stable processes, NIG-processes, GH-distributions, and others. Criteria are given for the Lévy measures which imply corresponding comparison results for European type options in (exponential) Lévy models. 相似文献
13.
In this paper we study the behaviour in time of the trace (the partition function) of the heat semigroup associated with symmetric stable processes in domains of R d . In particular, we show that for domains with the so called R-smoothness property the second terms in the asymptotic as t → 0 involves the surface area of the domain, just as in the case of Brownian motion. 相似文献
14.
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their p-variation indices. Exponential stock models driven by tempered stable processes are discussed as well. 相似文献
15.
16.
For any , a truncated symmetric α-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality
for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions
which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for
which the boundary Harnack principle fails.
The research of Panki Kim is supported by Research Settlement Fund for the new faculty of Seoul National University. The research
of Renming Song is supported in part by a joint US-Croatia grant INT 0302167. 相似文献
17.
《Stochastic Processes and their Applications》1987,24(1):1-18
We derive spectral necessary and sufficient conditions for stationary symmetric stable processes to be metrically transitive and mixing. We then consider some important classes of stationary stable processes: Sub-Gaussian stationary processes and stationary stable processes with a harmonic spectral representation are never metrically transitive, the latter in sharp contrast with the Gaussian case. Stable processes with a harmonic spectral representation satisfy a strong law of large numbers even though they are not generally stationary. For doubly stationary stable processes, sufficient conditions are derived for metric transitivity and mixing, and necessary and sufficient conditions for a strong law of large numbers. 相似文献
18.
John Hawkes 《Probability Theory and Related Fields》1998,112(1):1-11
Exact results are proved for the capacity of pullbacks of analytic sets by stable processes.
Received: 25 May 1988 / Revised version: 15 September 1997 相似文献
19.
Statistical Inference for Stochastic Processes - Jump processes driven by $$\alpha $$ -stable Lévy processes impose inferential difficulties as their increments are heavy-tailed and the... 相似文献
20.
LetB be a separable Banach space and let {:||1} denote the unit ball ofB
*. LetX be a symmetricp-stableB-valued random variable and let {X
j
}
j=1
n
be i.i.d. copies ofX. LetB
1 be a finite-dimensional Banach space with a symmetric unconditional basis {y
j
}
j=1
n
. An upper bound is obtained for
that improves the one given by Giné, Marcus and Zinn [J. Functional Anal.
63, 47–73 (1985)]. 相似文献