Heavy tails of a Lévy process and its maximum over a random time interval

2011 ◽  
Vol 54 (9) ◽  
pp. 1875-1884
Author(s):  
Yan Liu ◽  
QiHe Tang
Keyword(s):  
Lévy Process ◽  
Heavy Tails ◽  
Levy Process ◽  
Random Time ◽  
Time Interval ◽  
Random Time Interval

Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Sadibou Aidara ◽  
Ahmadou Bamba Sow
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Levy Process ◽  
Uniqueness Of Solution ◽  
Time Interval ◽  
Poisson Measure ◽  
Doubly Stochastic

AbstractIn this work we deal with a anticipated backward doubly stochastic differential equation associated to a random Poisson measure. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients. The novelty of our result lies in the fact that we allow the time interval to be infinite.

Impairment of Saccadic Eye Movements by Scopolamine Treatment

1993 ◽  
Vol 76 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Giulia A. Oliva ◽  
Maria P. Bucci ◽  
Roberto Fioravanti
Keyword(s):  
Eye Movements ◽  
Intramuscular Injection ◽  
Peak Velocity ◽  
Saccadic Eye Movements ◽  
Random Time ◽  
Time Interval ◽  
Random Time Interval ◽  
Standard Deviations

The effects of Scopolamine on the dynamics of saccadic eye movements, stimulated over a random time interval, have been investigated in humans. A 0.5-mg dose of the drug (intramuscular injection) had various influences on the basic saccadic parameters. For all subjects duration increased and peak velocity decreased, while for 50% of the subjects saccades became hypometric and latency increased. Standard deviations increased consistently too. Moreover, the Scopolamine treatment affected postsaccadic fixation; at the end of many saccades, the eye drifted considerably, but stability was recovered after a few seconds.

On a Lévy process pinned at random time

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed Erraoui ◽  
Astrid Hilbert ◽  
Mohammed Louriki
Keyword(s):  
Lévy Process ◽  
Markov Property ◽  
Levy Process ◽  
Random Time ◽  
Natural Filtration ◽  
The Right

AbstractIn this paper, our first goal is to rigorously define a Lévy process pinned at random time. Our second task is to establish the Markov property with respect to its completed natural filtration and thus with respect to the usual augmentation of the latter. The resulting conclusion is the right-continuity of completed natural filtration. Certain examples of such process are considered.

Skunks and gray foxes in a tropical dry region: casual or positive interactions?

Mammalia ◽  
2020 ◽  
Vol 84 (5) ◽  
pp. 469-474
Author(s):  
Gabriela Pérez-Irineo ◽  
Salvador Mandujano ◽  
Eva López-Tello
Keyword(s):  
Biosphere Reserve ◽  
Camera Traps ◽  
Random Time ◽  
Positive Interactions ◽  
Time Interval ◽  
Urocyon Cinereoargenteus ◽  
Random Time Interval ◽  
Overlap Coefficient ◽  
Total Effort ◽  
Negative Interactions

AbstractPrevious studies have shown that skunks present negative interactions with foxes. However, recently published observations have demonstrated that southern spotted skunk (Spilogale angustifrons) individuals follow gray foxes (Urocyon cinereoargenteus) in the Tehuacán-Cuicatlán Biosphere Reserve (TCBR) in Mexico. In this paper, we reported the same interaction in other locations in the TCBR and evaluated whether this interaction is casual or statistically positive. In this analysis, we included data pertaining to three skunk species (S. angustifrons, Conepatus leuconotus, and Mephitis macroura) and U. cinereoargenteus. We sampled 172 sites using camera traps from 2011 to 2018 for a total effort of 49,764 trap-days. The four studied species were nocturnal; the overlap coefficient between foxes and skunks varied from 0.70 to 0.83. Of the 32 consecutive records between S. angustifrons and U. cinereoargenteus, 11 showed that individuals of this skunk species closely followed U. cinereoargenteus and that these encounters were not random (time interval <1 min). We did not find evidence of a behavioral association of U. cinereoargenteus with C. leuconotus and M. macroura.

scholarly journals Nonparametric estimation of time-changed Lévy models under high-frequency data

2009 ◽  
Vol 41 (04) ◽  
pp. 1161-1188
Author(s):  
José E. Figueroa-López
Keyword(s):  
Lévy Process ◽  
Asymptotic Properties ◽  
Kernel Estimation ◽  
Uniform Boundedness ◽  
Building Blocks ◽  
Levy Process ◽  
Time Interval ◽  
Discrete Observations ◽  
Lévy Measure ◽  
Ergodic Diffusion

Let {Zt}t≥0be a Lévy process with Lévy measure ν, and let τ(t)=∫0tr(u)du, where {r(t)}t≥0is a positive ergodic diffusion independent fromZ. Based upon discrete observations of the time-changed Lévy processXt≔Zτtduring a time interval [0,T], we study the asymptotic properties of certain estimators of the parameters β(φ)≔∫φ(x)ν(dx), which in turn are well known to be the building blocks of several nonparametric methods such as sieve-based estimation and kernel estimation. Under uniform boundedness of the second moments ofrand conditions on φ necessary for the standard short-term ergodic property limt→ 0E φ(Zt)/t= β(φ) to hold, consistency and asymptotic normality of the proposed estimators are ensured when the time horizonTincreases in such a way that the sampling frequency is high enough relative toT.

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