Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

On Utility Maximization with Random Interval Payoffs

This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.

Stability Analysis of Robust Arbitrage in a Random Interval Valued Financial Market

Stability of robust arbitrage under different probability measures is discussed in a random interval valued financial market.In a fundamental financial market without robust arbitrages, a suitable condition is given to guarantee that the market with new probability measures will also have no robust arbitrage. In order to specify the result got in this article,an example of binomial tree financial model with interval ratios of change is proposed.

Fuzzy norm method for evaluating random vibration of airborne platform from limited PSD data

For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.

Efficient adaptive Kriging for system reliability analysis with multiple failure modes under random and interval hybrid uncertainty

In the field of the system reliability analysis with multiple failure modes,the advances mainly involve only random uncertainty.The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty(RI-HU).At present,there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability.This paper proposed an efficient Kriging model based on numerical simulation algorithm to solve the system reliability analysis under RI-HU.This method proposes a system learning function to train the system Kriging models of the system limit state surface.The convergent Kriging models are used to replace the limit state functions of the system multi-mode for identifying the state of the random sample.The proposed system learning function can adaptively select the failure mode contributing most to the system failure probability from the system and update its Kriging model.Thus,the efficiency of the Kriging training process can be improved by avoiding updating the Kriging models contributing less to estimating the system failure probability.The presented examples illustrate the superiority of the proposed method.

On the compensator of the default process in an information-based model

This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.