In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
Let X=(X) be a two-parameter *-Markov process with a transition function (p1, p2, p), where X, takes values in the state space (Er,), T=[0,)2. For each r T, let f, be a measurable transformation of (E,) into the state...Let X=(X) be a two-parameter *-Markov process with a transition function (p1, p2, p), where X, takes values in the state space (Er,), T=[0,)2. For each r T, let f, be a measurable transformation of (E,) into the state space (E’r, ). Set Y,=f,(X,), r T. A sufficient condition is given for the process Y=(Yr) still to be a two-parameter *-Markov process with a transition function in terms of transition function (p1, p2, p) and fr. For *-Markov families of two-parameter processes with a transition function, a similar problem is also discussed.展开更多
In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
I. INTRODUCTION AND DEFINITIONS In this report, we shall give a simple counterexample to negative Theorem 1 and Proposition 3 (c)(ii)in [1] and explain the difference between the large-past Markov property and *-Marko...I. INTRODUCTION AND DEFINITIONS In this report, we shall give a simple counterexample to negative Theorem 1 and Proposition 3 (c)(ii)in [1] and explain the difference between the large-past Markov property and *-Markov property. Thereby some mistakes are cleared up.展开更多
Given (Ω, (?), P ), let ∧ be a nonnegative additional set function on R_+~2 and have density function λ about Lebesgue measure l. For simplicity, in this report, we always suppose that there exists a constant M】0 ...Given (Ω, (?), P ), let ∧ be a nonnegative additional set function on R_+~2 and have density function λ about Lebesgue measure l. For simplicity, in this report, we always suppose that there exists a constant M】0 such that d∧/dl=λ≤M.展开更多
Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.
A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing th...A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems, is presented in the paper. The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.展开更多
Using the plot of growing single-parameter Markov processes on a single-parameter Markov process, we constructed successfully a class of important two-parameter processes which are called MM-class processes and whose ...Using the plot of growing single-parameter Markov processes on a single-parameter Markov process, we constructed successfully a class of important two-parameter processes which are called MM-class processes and whose two parameters are unequal in status. We have researched if MM-class processes possess the various two-parameter Markov properties. The definitions of the latter can be found in refs. [1]—[3]. For the definition of the展开更多
Let (Ω,(?), P) be a complete probability space with a family of sub-σ-fields {(?)_z}_z∈R_+~2 which satisfies the usual conditions. Yeh considered the existence and uniqueness of strong solutions of the following no...Let (Ω,(?), P) be a complete probability space with a family of sub-σ-fields {(?)_z}_z∈R_+~2 which satisfies the usual conditions. Yeh considered the existence and uniqueness of strong solutions of the following non-Markovian stochastic differential equations (SDE)展开更多
Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief re...Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief review of RAM and presents a few examples where the model arises. An extended discussion will focus a concrete model, the GEM distribution, and its ordered analogue, the Poisson-Dirichlet distribution. The paper concludes with a discussion of the GEM process.展开更多
Ⅰ. INTRODUCTION AND DEFINITIONS When we consider different pasts, there are various definitions of Markov properties for twoparameter processes. Even if we only consider the wide-past, there are still several definit...Ⅰ. INTRODUCTION AND DEFINITIONS When we consider different pasts, there are various definitions of Markov properties for twoparameter processes. Even if we only consider the wide-past, there are still several definitions of Markov properties, for example, the *-Markov property in [1], the wide-past Markov property in [2] and another wide-past Markov property given in [3] and the one展开更多
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
基金Project supported by the National Natural Science Foundation of Chinathe Guangdong Provincial Natural Science Foundation of China the Foundation of Zhongshan University Advanced Research Center.
文摘Let X=(X) be a two-parameter *-Markov process with a transition function (p1, p2, p), where X, takes values in the state space (Er,), T=[0,)2. For each r T, let f, be a measurable transformation of (E,) into the state space (E’r, ). Set Y,=f,(X,), r T. A sufficient condition is given for the process Y=(Yr) still to be a two-parameter *-Markov process with a transition function in terms of transition function (p1, p2, p) and fr. For *-Markov families of two-parameter processes with a transition function, a similar problem is also discussed.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10131040)China Postdoctoral Science Foundation.
文摘In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.
文摘I. INTRODUCTION AND DEFINITIONS In this report, we shall give a simple counterexample to negative Theorem 1 and Proposition 3 (c)(ii)in [1] and explain the difference between the large-past Markov property and *-Markov property. Thereby some mistakes are cleared up.
文摘Given (Ω, (?), P ), let ∧ be a nonnegative additional set function on R_+~2 and have density function λ about Lebesgue measure l. For simplicity, in this report, we always suppose that there exists a constant M】0 such that d∧/dl=λ≤M.
基金Partially supported by the ANR grant "Masterie" BLAN 012103Support by the CNCS grant "PN-II-ID-PCE-2011-3-0593"
文摘Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.
文摘A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems, is presented in the paper. The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.
基金Project supported by the National Natural Science Foundation of China
文摘Using the plot of growing single-parameter Markov processes on a single-parameter Markov process, we constructed successfully a class of important two-parameter processes which are called MM-class processes and whose two parameters are unequal in status. We have researched if MM-class processes possess the various two-parameter Markov properties. The definitions of the latter can be found in refs. [1]—[3]. For the definition of the
文摘Let (Ω,(?), P) be a complete probability space with a family of sub-σ-fields {(?)_z}_z∈R_+~2 which satisfies the usual conditions. Yeh considered the existence and uniqueness of strong solutions of the following non-Markovian stochastic differential equations (SDE)
基金This work was supported by the Natural Science and Engineering Research Council of Canada.
文摘Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief review of RAM and presents a few examples where the model arises. An extended discussion will focus a concrete model, the GEM distribution, and its ordered analogue, the Poisson-Dirichlet distribution. The paper concludes with a discussion of the GEM process.
文摘Ⅰ. INTRODUCTION AND DEFINITIONS When we consider different pasts, there are various definitions of Markov properties for twoparameter processes. Even if we only consider the wide-past, there are still several definitions of Markov properties, for example, the *-Markov property in [1], the wide-past Markov property in [2] and another wide-past Markov property given in [3] and the one
