Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.     

Gating processes in Na-channel of biological membrane from the standpoint of superionic phase transition

The method of condensed matter physics is applied to reason out the problem of Na transport through a biological membrane. A similiarity of gating process in Na ion channel to the superionic phase transition is discussed. A possible microscopic mechanism is suggested.     

沉淀法制备CeO2超微粉末

采用过氧化氢－－氨水沉淀法在较低温度下制备ＣｅＯ２超微粉末。试验表明，溶液起始浓度及焙烧温度以形成粉素晶体粒径有一定影响。焙烧温度在２２０－８５０℃，所得ＣｅＯ２微粉均为立方晶系，透射电测试表明，粒子基本呈球形，晶体平均粒径随焙烧温度升高而增大。控制适当条件，可制得粒径范围在５－１３ｎｍ，比表面积１１１．８ｍ＾２／ｇ的ＣｅＯ２超微粉末。     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Estimation of entropy and other functionals of a multivariate density

For a multivariate density f with respect to Lebesgue measure , the estimation of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGkbGaaiikaiaadAgacaGGPaGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!4404!\[\int {J(f)fd\mu } \], and in particular % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbWaaWbaaSqabeaacaaIYaaaaOGaamizaiabeY7a% TbWcbeqab0Gaey4kIipaaaa!41E4!\[\int {f^2 d\mu } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbGaciiBaiaac+gacaGGNbGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!44AC!\[\int {f\log fd\mu } \], is studied. These two particular functionals are important in a number of contexts. Asymptotic bias and variance terms are obtained for the estimators % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcacaWGKbGaamOramaaBaaaleaacaWGobaabeaaaeqabeqd% cqGHRiI8aaaa!4994!\[\mathop I\limits^ \wedge = \int {J(\mathop f\limits^ \wedge )dF_N } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaeSipIOdaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWG% KbGaeqiVd0galeqabeqdcqGHRiI8aaaa!4C40!\[\mathop I\limits^ \sim = \int {J(\mathop f\limits^ \wedge )\mathop f\limits^ \wedge d\mu } \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGMbaaaaaa!3E9C!\[{\mathop f\limits^ \wedge }\] is a kernel density estimate of f and F _n is the empirical distribution function based on the random sample X ₁ ,..., X _n from f. For the two functionalsmentioned above, a first order bias term for Î can be made zero by appropriate choices of non-unimodal kernels. Suggestions for the choice of bandwidth are given; for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWGKbGaam% OramaaBaaaleaacaWGobaabeaaaeqabeqdcqGHRiI8aaaa!476C!\[\mathop I\limits^ \wedge = \int {\mathop f\limits^ \wedge dF_N } \], a study of optimal bandwidth is possible.This research was supported by an NSERC Grant and a UBC Killam Research Fellowship.     

Size distribution of fractured areas in one-dimensional systems

We study a one-dimensional model for fracture, identifying fractured areas with intervals on which a stress field exceeds a threshold value. When is a diffusion process, the cumulative numberN(l) of fractured areas whose length is greater thanl obeys a power lawCl ^–p asl0 with probability one. The exponentp and the constantC are determined. The exponentp agrees with the Hausdorff dimension of the end points of fractured areas, i.e., ^–1(). Even if is self-similar with parameterH>0, i.e.,(cx)– is equivalent toc ^H {(x)–} for anyc>0, the exponentp does not depend solely onH;p=H, where(0, 1/H) is another parameter characterizing. Non-diffusion processes are given whereN(l) does not follow a power law.     

Front propagation in certain one-dimensional exclusion models

Recent results on two interacting particle systems on are summarized, the asymmetric simple exclusion process and the branching exclusion process.     

Pressure and temperature effects on the excess deuteron and proton conductance

The limiting molar conductances ° of deuterium chloride DCl in D₂O were determined as a function of pressure and temperature in order to examine the proton-jump mechanism in detail. The excess deuteron conductances °_E(D ⁺), as estimated by the equation [°_E(D ⁺) = °(DCl/D ₂ O) – °(KCl/D ₂ O)], increases with an increase in the pressure and temperature as well as the excess proton conductance [°_E(H ⁺) = °(HCl/H ₂ O) – °(KCl/H ₂ O)]. The isotope effect on the excess conductances, however, depends on the pressure and temperature contrary to the model proposed by Conway et al.: °_E(H ⁺)/°_E(D ⁺) decreases with increasing pressure and temperature. The magnitude of the decrease with pressure becomes more prominent at lower temperature. These results are discussed in terms of the pre-rotation of adjacent water molecules, the bending of hydrogen bonds with pressure, and the difference in strength of hydrogen bonds between D₂O and H₂O.