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1.
E. Mathieu Y. Foucher P. Dellamonica J. P. Daures 《Methodology and Computing in Applied Probability》2007,9(3):389-397
In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical
taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In
this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding
the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed.
A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented
for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct
times and follow-up has an impact on the evolution of patients.
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2.
本文讨论半马氏环境连续时间马氏决策过程中的平均准则.首先讨论了半马氏报酬过程中的逼近问题,进而讨论平均目标函数逼近问题。 相似文献
3.
Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications. 相似文献
4.
This paper deals with the averaging and diffusion approximation for occupation time of general phase space semi-Markov processes under split with simple and double merging in a series scheme. These results seem to be particularly interesting since the variance coefficient is obtained in a simple form. The method of proof of weak convergence results here is based on the construction of the compensating operator of the extended Markov renewal processes and on the solution of the singular perturbation problem of this operator acting on test functions. 相似文献
5.
《Journal of computational and graphical statistics》2013,22(4):907-929
Importance sampling methods can be iterated like MCMC algorithms, while being more robust against dependence and starting values. The population Monte Carlo principle consists of iterated generations of importance samples, with importance functions depending on the previously generated importance samples. The advantage over MCMC algorithms is that the scheme is unbiased at any iteration and can thus be stopped at any time, while iterations improve the performances of the importance function, thus leading to an adaptive importance sampling. We illustrate this method on a mixture example with multiscale importance functions. A second example reanalyzes the ion channel model using an importance sampling scheme based on a hidden Markov representation, and compares population Monte Carlo with a corresponding MCMC algorithm. 相似文献
6.
In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes. 相似文献
7.
In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims, in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes. 相似文献
8.
A. Jaśkiewicz 《Journal of Optimization Theory and Applications》2009,141(2):321-347
Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded,
payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result
concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point
argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value.
In addition, one player possesses an ε-optimal stationary strategy (ε>0), whereas the other has an optimal stationary strategy.
A. Jaśkiewicz is on leave from Institute of Mathematics and Computer Science, Wrocław University of Technology.
This work is supported by MNiSW Grant 1 P03A 01030. 相似文献
9.
The aim of this paper is the presentation of new models for option pricing that are discrete in time and in the framework of Markov and semi-Markov processes as an alternative to the classical Cox–Rubinstein model, and that also allow the possibility of arbitrage. Both cases of European and American options are considered and possible extensions are given. © 1997 by John Wiley & Sons, Ltd. 相似文献
10.
Qi-Ming He 《Queueing Systems》2005,49(3-4):363-403
In this paper, we study a discrete time queueing system with multiple types of customers and a first-come-first-served (FCFS) service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual customers have PH-distributions. A GI/M/1 type Markov chain for a generalized age process of batches of customers is introduced. The steady state distribution of the GI/M/1 type Markov chain is found explicitly and, consequently, the steady state distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. We show that the generalized age process and a generalized total workload process have the same steady state distribution. We prove that the waiting times and sojourn times have PH-distributions and find matrix representations of those PH-distributions. When the arrival process is a Markov arrival process with marked transitions, we construct a QBD process for the age process and the total workload process. The steady state distributions of the waiting times and the sojourn times, both at the batch level and the customer level, are obtained from the steady state distribution of the QBD process. A number of numerical examples are presented to gain insight into the waiting processes of different types of customers.AMS subject classification: 60K25, 60J10This revised version was published online in June 2005 with corrected coverdate 相似文献