We present CCMC (Conditional CSL Model Checker), a model checker for continuous-time Markov chains (CTMCs) with respect to properties specified in continuous-time stochastic logic (CSL). Existing CTMC model checkers such as PRISM or MRMC handle only binary CSL until path formulas. CCMC is the first tool that supports algorithms for analyzing multiple until path formulas. Moreover, CCMC supports...

The predominant technique for computing the transient distribution of a Continuous Time Markov Chain (CTMC) exploits uniformization, which is known to be stable and efficient for non-stiff to mildly-stiff CTMCs. On stiff CTMCs however, uniformization suffers from severe performance degradation. In this paper, we report on our observations and analysis of an alternative technique using Krylov su...

Rough volatility models have recently been empirically shown to provide a good fit historical time series and implied smiles of SPX options. They are continuous-time stochastic models, whose process is driven by fractional Brownian motion with Hurst parameter less than half. Due the challenge that it neither semimartingale nor Markov process, there no unified method not only applies all rough b...

Abstract Lithofacies prediction can facilitate the search for hydrocarbon reservoirs and is, therefore, crucial seismic exploration. We proposed a new approach lithofacies based on stochastic simulation of pseudo-wells. First, we performed pseudo-well using continuous-time Markov chain (CTMC), which accurately describe geological deposition be created logging, core or data. used CTMC to randoml...

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMC...

We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price options under general one-dimensional processes. prove convergence setting obtain sharp estimate rate for diffusion models. Our theoretical analysis reveals how design grid CTMC achieve faster convergence. Numerical experiments are conducted demonstrate accura...

We explore Bayesian analysis for continuous-time Markov chain (CTMC) models based on a conditional reference prior. For CTMC models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition to the elapsed time, a...

This supporting information file presents the sensitivity bounds (SBs) from an information theory perspective. The general SBs (both transient and stationary) are obtained by a limiting process on the relative entropy between path distributions. The information theory perspective provides also intuitive and explicit formulas for the quantities of interest for both Discrete Time Markov Chains (D...

The counterexample in probabilistic model checking (PMC) is a set of paths in which a path formula holds, and their accumulated probability violates the probability bound. However, understanding the counterexample is not an easy task. In this paper we address the complementary task of counterexample generation, which is the counterexample analysis. We propose an aided-diagnostic method for prob...

Prevalent approaches to software reliability model-ing are black-box based, i.e., the the software system is considered as a whole and only its interactions with the outside world are modeled without looking into its internal structure. However, with the advancement and widespread use of object oriented systems design and development, the use of component-based software development is on the ri...