Papers by Narn-Rueih Shieh
Bulletin of The London Mathematical Society, 1990
We describe explicit conditions on the transition density functions of a time-homogeneous continu... more We describe explicit conditions on the transition density functions of a time-homogeneous continuous Markov process so that almost every path has multiple points. The application to two-and threedimensional diffusions is exhibited.
We prove a uniform asymptotic law for the branching measure on the boundary of a Galton-Watson tr... more We prove a uniform asymptotic law for the branching measure on the boundary of a Galton-Watson tree, which is consistent with certain well-known uniform laws associated with Brownian motions. We also list a certain spectrum formula arising from this uniform law. *
Let X = {X(t), t ∈ R N } be a random field with values in R d . We develop measure theoretic meth... more Let X = {X(t), t ∈ R N } be a random field with values in R d . We develop measure theoretic methods for determining the Hausdorff and packing dimensions of the image X(E) for any given closed set E ⊂ R N . We show that these results are applicable to Gaussian random fields, self-similar stable random fields with stationary increments, the (N, d)-stable sheets and the Rosenblatt process.
FRACTAL GEOMETRY OF LÉVY-BASED SPATIAL-TEMPORAL RANDOM FIELDS
Fractals-complex Geometry Patterns and Scaling in Nature and Society, 2009
Abstract: Let X={X (t, x), t??? ???, x??? ??? d} be a L??vy-based spatial-temporal random field p... more Abstract: Let X={X (t, x), t??? ???, x??? ??? d} be a L??vy-based spatial-temporal random field proposed by Barndorff???Nielsen and Schmiegel 1 for dynamic modeling of turbulence. We describe some fractal geometry for this field, with a view toward a proper non-Gaussian ...
Multiple points of fractional stable processes
Journal of Mathematics of Kyoto University, 1993
... previous :: next. Multiple points of fractional stable processes. Narn-Rueih Shieh. Source: J... more ... previous :: next. Multiple points of fractional stable processes. Narn-Rueih Shieh. Source: J. Math. Kyoto Univ. Volume 33, Number 3 (1993), 731-741. Primary Subjects: 60G17. Secondary Subjects: 60J55. Full-text: Access by subscription. PDF File (1152 KB). Links and Identifiers ...
Limit theorems for local times of fractional Brownian motions and some other self-similar processes
Journal of Mathematics of Kyoto University, 1996
English | 正體中文 | 简体中文 | 全文筆數/總筆數 : 55767/175375 造訪人次 : 3437663 線上人數 : 86. RC Version 4.0 © Powere... more English | 正體中文 | 简体中文 | 全文筆數/總筆數 : 55767/175375 造訪人次 : 3437663 線上人數 : 86. RC Version 4.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team. 搜尋範圍 全部NTUR 進階搜尋. ...
Collisions of Markov Processes
Tokyo Journal of Mathematics, 1995
Let $X_1$ and $X_2$ be two independent Hunt processes which take values in a metric space and hav... more Let $X_1$ and $X_2$ be two independent Hunt processes which take values in a metric space and have the same transition density functions with respect to a reference measure. We describe explicit conditions on the transition density functions so that $X_1$ and $X_2$ have ...
Let ${\bf{w}}(t,x):=(u,v)(t,x),\ t>0,\ x\in \mathbb{R}^{n},$ be the $\mathbb{R}^2$-valued spatial... more Let ${\bf{w}}(t,x):=(u,v)(t,x),\ t>0,\ x\in \mathbb{R}^{n},$ be the $\mathbb{R}^2$-valued spatial-temporal random field ${\bf{w}}=(u, v)$ arising from a certain two-equation system of fractional kinetic equations of reaction-diffusion type, with given random initial data $u(0,x)$ and $v(0,x).$ The space-fractional derivative is characterized by the composition of the inverses of the Riesz potential and the Bessel potential. We discuss two scaling limits, the macro and the micro, for the homogenization of ${\bf{w}}(t,x)$, and prove that the rescaled limit is a singular field of multiple It\^{o}-Wiener integral type, subject to suitable assumptions on the random initial conditions. In the two scaling procedures, the Riesz and the Bessel parameters play distinctive roles. Moreover, since the component fields $u,v$ are dependent on the interactions present within the system, we employ a certain stochastic decoupling method to tackle this components dependence. The time-fractional system is also considered, in which the Mittag-Leffler function is used.
Stochastics An International Journal of Probability and Stochastic Processes, 2012
We study the correlation decay and the expected maximal increments of the exponential processes d... more We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (p, q). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (p, q). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.
Multifractal Products of Stationary Diffusion Processes
Stochastic Analysis and Applications, 2009
We investigate the properties of multifractal products of the exponential of stationary diffusion... more We investigate the properties of multifractal products of the exponential of stationary diffusion processes defined by stochastic differential equations with linear drift and certain form of the diffusion coefficient corresponding to a variety of marginal distributions. The conditions on ...
Proceedings of The American Mathematical Society, 2009
We study precise conditions for mutual absolute continuity and mutual singularity of two random -... more We study precise conditions for mutual absolute continuity and mutual singularity of two random -adic Riesz products, defined respectively by two sequences of coefficients , . Our conditions and assertions are specific to the -adic case. We also calculate explicitly the Hausdorff dimension, and in case the defining coefficients are constant, we have an integral representation of the dimension formula with a rapid convergence rate − .
Multiple Points of a Random Field
Proceedings of The American Mathematical Society, 1984
ABSTRACT. We prove that a d-dimensional random field X = {X(t)}teRN has uncountably many r-multip... more ABSTRACT. We prove that a d-dimensional random field X = {X(t)}teRN has uncountably many r-multiple points as when it satisfies Pitt's (Ar) con-dition [9). Those t's for which X(t) hits the multiple point can be separated by any given positive number, and multiple points can occur while ...
A Lil for Occupation Times of Stable Processes
Proceedings of The American Mathematical Society, 1987
1. Introduction and main result. The purpose of this paper is to prove a Strassen-type law of ite... more 1. Introduction and main result. The purpose of this paper is to prove a Strassen-type law of iterated logarithms for the occupation times of a stable process. First, we review the result in Donsker and Varadhan [3] which is our motivation for study. Let {x(s),0 < s < 00} be Brownian ...
Let X1, . . . , XN denote N independent, symmetric Lévy processes on R d . The corresponding addi... more Let X1, . . . , XN denote N independent, symmetric Lévy processes on R d . The corresponding additive Lévy process is defined as the following N -parameter random field on R d :
Local times and related sample Path properties of certain self-similar processes
Kyoto Journal of Mathematics, 1993
... Local times and related sample Path properties of certain self-similar processes. Norio Kôno ... more ... Local times and related sample Path properties of certain self-similar processes. Norio Kôno and Narn-Rueih Shieh. Source: J. Math. Kyoto Univ. Volume 33, Number 1 (1993), 51-64. Primary Subjects: 60G17. Secondary Subjects ...
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2011
By using a wavelet method we prove that the harmonisable-type N -parameter multifractional Browni... more By using a wavelet method we prove that the harmonisable-type N -parameter multifractional Brownian motion (mfBm) is a locally nondeterministic Gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.
Simulation of multifractal products of Ornstein-Uhlenbeck type processes
Nonlinearity, 2010
This paper investigates and provides evidence of the multifractal properties of products of the e... more This paper investigates and provides evidence of the multifractal properties of products of the exponential of Ornstein???Uhlenbeck processes driven by L??vy motion. We demonstrate in detail the construction of a multifractal process with gamma subordinator as the ...
Proceedings of The American Mathematical Society, 1989
Let X , Y be two independent Levy processes in R . We describe simple conditions on the density f... more Let X , Y be two independent Levy processes in R . We describe simple conditions on the density functions of X , Y which guarantee that the paths X(-), Y(-) will have uncountably many collisions almost surely.
Hausdorfi and Packing Dimension Results for Self-similar Random Fields
Electronic Journal of Probability, 2009
We study the correlation decay and the expected maximal increment (Burkholder-Davis-Gundy type in... more We study the correlation decay and the expected maximal increment (Burkholder-Davis-Gundy type inequalities) of the exponential process determined by a fractional Ornstein-Uhlenbeck process. The method is to apply integration by parts formula on integral representations of fractional Ornstein-Uhlenbeck processes, and also to use Slepian's inequality. As an application, we attempt Kahane's T-martingale theory based on our exponential process which is shown to be of long memory.
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Papers by Narn-Rueih Shieh