Showing papers by "Barbara Martinucci published in 2021"
TL;DR: In this article, the authors analyzed the one-dimensional telegraph random process confined by two boundaries, 0 and H > 0, and provided various results on the expected values of the renewal cycles and of the absorption time.
Abstract: We analyze the one-dimensional telegraph random process confined by two boundaries, 0 and H > 0. The process experiences hard reflection at the boundaries (with random switching to full absorption). Namely, when the process hits the origin (the threshold H) it is either absorbed, with probability α, or reflected upwards (downwards), with probability 1 − α, for 0 < α < 1. We provide various results on the expected values of the renewal cycles and of the absorption time. The adopted approach is based on the analysis of the first-crossing times of a suitable compound Poisson process through linear boundaries. Our analysis includes also some comparisons between suitable stopping times of the considered telegraph process and of the corresponding diffusion process obtained under the classical Kac’s scaling conditions.
6 citations
TL;DR: In this paper, Crescenzo et al. studied the asymptotic behavior of the absorption time at the origin with respect to two different scalings: $x\to \infty $676 in the first case; $mu \to \INfty $672 in the second case.
Abstract: We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see eg Di Crescenzo et al (Methodol Comput Appl Probab 20:333–352 2018)) It is a particular random motion with finite velocity which starts at x ≥ 0, and its dynamics is determined by upward and downward switching rates λ and μ, with λ > μ, and an absorption probability (at the origin) α ∈ (0,1] Our aim is to study the asymptotic behavior of the absorption time at the origin with respect to two different scalings: $x\to \infty $
in the first case; $\mu \to \infty $
, with λ =β μ for some β > 1 and x > 0, in the second case We prove several large and moderate deviation results We also present numerical estimates of β based on an asymptotic Normality result for the case of the second scaling
4 citations
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TL;DR: In this paper, the jump telegraph process was considered and the incomplete financial market model based on this process was studied, which can price switching risks as well as jump risks of the model.
Abstract: We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.
01 Jan 2021
TL;DR: In this paper, the authors considered continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates and gave explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process.
Abstract: We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364].
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TL;DR: In this article, the authors identify a model able to describe the fluctuations of the soil temperatures monitored in the volcanic caldera of the Campi Flegrei area in Naples (Italy).
Abstract: The aim of this research is to identify a model able to describe the fluctuations of the soil temperatures monitored in the volcanic caldera of the Campi Flegrei area in Naples (Italy). The study focuses on the data concerning the temperatures in the mentioned area through a seven-year period (cf. Sabbarese et al. [14]). The deterministic component of the model, given by the seasonal trend of the temperatures, is obtained through a regression method on the time series. A fractional Brownian motion (fBm) is chosen to represent the residual process between the seasonal trend and the time series. This is validated through a suitable test and an estimation based on the periodogram of the data. Thereafter, the Hurst exponent of the process is estimated by means of a method proposed by Cannon et al. [2]. Finally, an inference test based on the detrended moving average of the data is adopted in order to confirm that the residual series follows a fBm.
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TL;DR: In this paper, the authors investigated the one-dimensional telegraph random process in the presence of an elastic boundary at the origin and obtained the distribution of the renewal cycles and of the absorption time.
Abstract: We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability $\alpha$, or reflected upwards, with probability $1-\alpha$. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.