相关论文: Extreme times for volatility processes

The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which…

When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian random variable. In a recent paper by the three first…

How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the…

The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…

We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…

We examine the density functions of the first exit times of the Bessel process from the intervals [0,1) and (0,1). First, we express them by means of the transition density function of the killed process. Using that relationship we provide…

In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…

We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…

During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…

Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…

In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in…

Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…

The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…

We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…

The statistics of the slowest first-passage time among a large population of $N$ searchers is crucial for determining the completion time of many stochastic processes. Classical extreme-value theory predicts that for diffusing particles in…

Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…

Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations.…

A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time \tau the random walk reaches a given level. Specifically, the p-moment…