• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제11권6호
• /
• pp.3273-3308
• /
• 2017

Building appropriate trust evaluation models is an important research issue for security guarantee in social networks. Most of the existing works usually consider the trust values at the current time slot, and model trust as the stochastic variable. However, in fact, trust evolves over time, and trust is a stochastic process. In this paper, we propose a novel time-variant stochastic trust evaluation (TSTE) model, which models trust over time and captures trust evolution by a stochastic process. Based on the proposed model, we derive the time-variant bound of untrustworthy probability, which provides stochastic trust guarantee. On one hand, the time-variant trust level of each node can be measured by our model. Meanwhile, by tolerating nodes with relatively poor performance, our model can effectively improve the node resource utilization rate. Numerical simulations are conducted to verify the accuracy and consistency of the analytical bounds on distinguishing misbehaved nodes from normal ones. Moreover, simulation results on social network dataset show the tradeoff between trust level and resource utilization rate, and verify that the successful transmission rate can be improved by our model.

• Journal of the Korean Data and Information Science Society
• /
• 제21권6호
• /
• pp.1311-1317
• /
• 2010

A continuous time asymmetric power GARCH(1,1) model is suggested, based on a single background driving L$\'{e}$vy process. The stochastic differential equation for the given process is derived and the strict stationarity and kth order moment conditions are examined.

• 대한수학회보
• /
• 제44권4호
• /
• pp.807-816
• /
• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• International Journal of Reliability and Applications
• /
• 제4권1호
• /
• pp.1-12
• /
• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.

• Journal of the Korean Statistical Society
• /
• 제35권4호
• /
• pp.397-407
• /
• 2006

A new stochastic process is introduced for describing a mechanism of viruses. The process generalizes the $Bartoszy\'{n}ski's$ process ($Bartoszy\'{n}ski$, 1975a, 1975b, 1976) by allowing the stochastic perturbation between consecutive jumps to take into account the persistent infection (the infection without breaking infected cells). It is shown that the new process can be obtained by a weak limit of a sequence of Markov branching processes. Along with the construction of the new process, we study how the stochastic perturbation influences the risk of a symptom in an infected host. For this purpose, the quantal response model and the threshold model are investigated and compared through their induced survival functions.

• 대한수학회보
• /
• 제37권3호
• /
• pp.619-631
• /
• 2000

We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.

• 대한수학회지
• /
• 제38권3호
• /
• pp.657-667
• /
• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• 충청수학회지
• /
• 제12권1호
• /
• pp.133-146
• /
• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• 충청수학회지
• /
• 제17권2호
• /
• pp.197-203
• /
• 2004

We find some properties of a stochastic processX(t, ${\omega}$) ${\in}L^2_{s.a.p.}$ which is of bounded variation.

• Journal of Mechanical Science and Technology
• /
• 제20권5호
• /
• pp.652-657
• /
• 2006

Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and 1/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation.