An approximation of the first passage probability of systems under nonstationary random excitation

An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom （SDOF） linear systems under two special types of modulated white noise excitations.

First Passage Probability of Structures under Non-Gaussian Stochastic Behavior

An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

First passage probabilities of one-dimensional diffusion processes

This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.