We consider temporal aggregation of stationary and nonstationary time series with short memory, long memory and antipersistence, within the framework of fractional autoregressive processes. Asymptotically, long memory and antipersistence are preserved whereas short memory components vanish. In...

The article introduces a concept of probabilistic ecological competition from the aquatic hyacinth perspective, which often helps to track and analyze the sustainability of different species involved in the ecological system. A case study is presented to investigate the impact of the pH content...

In the paper we present a method of simulation of ruin probability over infinite horizon for fractional Brownian motion with parameter of self-similarity H ½. We derive some theoretical results which show how fast the method works. As an application of our method we numerically compute the...

In this article, we derive the first passage time (FPT) distribution and the mean first passage time (MFPT) of random walks from multiple sources on networks. On the basis of analysis and simulation, we find that the MFPT drops substantially when particle number increases at the first stage, and...

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time....

In the paper we present a method of simulation of ruin probability over infinite horizon for fractional Brownian motion with parameter of self-similarity H ½. We derive some theoretical results which show how fast the method works. As an application of our method we numerically compute the...