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
In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus...In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.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
A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of t...A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.展开更多
I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replac...I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replacement at each discrete-time point. The true state of the system is not known when it is operated. Instead, the system is monitored after operation and some incomplete information concerned with the deterioration is obtained for decision making. Since there are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis of our problem.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
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.
基金Supported by the National Natural Sci-ence Foundations of China (10271062 and 10471119)the Natural Science Foundation of Shandong Province(Y2004A06, Y2008A12, and ZR2009AL015)+1 种基金the Science Foundations of Shandong Provincial Education Department (J07yh05)the Science Foundations of Qufu Normal University (XJ0713, Bsqd200517)
文摘In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.
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A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.
文摘I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replacement at each discrete-time point. The true state of the system is not known when it is operated. Instead, the system is monitored after operation and some incomplete information concerned with the deterioration is obtained for decision making. Since there are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis of our problem.
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
