Symmetry properties of the Brownian motion and of some diffusion processes are useful to
specify the probability density functions and the first passage time density through specific …

For many high reliable products, the degradation can be characterized in terms of two
performance characteristics (PCs). Under this circumstance, both the degradation rates and …

With the aim of solving the reliability modeling and calculation of multivariate stochastic
degradation systems, two stochastic degradation models based on the bivariate Wiener …

Sample allocation and selection technology is of great significance in the test plan design of
prognostics validation. Considering the existing researches, the importance of prognostics …

The first passage time density of a diffusion process to a time varying threshold is of primary
interest in different fields. Here we consider a Brownian motion in presence of an …

Statistical models of price volatility most commonly use low-frequency (daily, weekly, or
monthly) returns. However, despite their availability, two types of financial data have not …

Estimating asset price volatilities is a common problem in finance; for example, accurate
estimates of volatility paths play a key role in both option pricing and portfolio design …

To conclude that FX r (ds)= q (s) ds, one still needs that FX r (ds) is absolutely continuous
with respect to Lebesgue measure. In [2], when a moving boundary is infinitely differentiable …

The first exit time (FET) problem for Gauss-Markov (GM) processes ([3]) plays a key role in
the construction and development of models in a wide variety of fields, such as mathematical …

The interdependency between the evolution of counterparty credit quality and the underlying
risk factor (s) driving the value of a derivative contract has led to wrong way/right way risk …