Each type of fishery has its own characteristic behavior, and understanding this condition is an important part of devel- oping and managing fishing operations comprehensively. Based on the random walk model, the rela...Each type of fishery has its own characteristic behavior, and understanding this condition is an important part of devel- oping and managing fishing operations comprehensively. Based on the random walk model, the relationship between distance and frequency distribution of adjacent fishing positions was analyzed by the Commission for Conservation of Antarctic Marine Living Resources (CCAMLR) Subareas 48.1, 48.2, and 48.3. The frequency of distances between consecutive hauls demonstrated a heavy- tailed distribution, which could be used to estimate the value of parameter μ in the power function F(l)~ l μ of a random walk model to determine the type of random walk patterns that characterize Chinese krill fishery. Results indicated that the fishing pattern of the Chinese krill fishery is consistent with the Lévy random walk model, with which the step-length is applied to analyze the walking pattern. When a defined walk in a space of dimension is greater than one, the steps made are in isotropic random directions. Fur- thermore, a strong and positive correlation between fishing behavior (using the parameter μ as an indicator) and catch per unit effort of the Chinese krill fishery was observed.展开更多
The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the ab...The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.展开更多
In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its loca...In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.展开更多
The analysis of animal movement patterns can provide important information on animals’ responses to habitat features. In this study, the movement paths of eastern chipmunks (<em>Tamias striatus</em>) were...The analysis of animal movement patterns can provide important information on animals’ responses to habitat features. In this study, the movement paths of eastern chipmunks (<em>Tamias striatus</em>) were examined in four landscapes, with different levels of habitat fragmentation, using either fluorescent powdering or spool-and-line tracking. Descriptions of the tree and ground vegetation communities were performed in the vicinity of the trail to obtain information on habitat use and habitat selection. Several key movement variables were calculated, including the total path length, net distance, fractal dimension, and radius of gyration. Despite statistically significant differences in some of the movement metrics between the four landscapes, the overall movement patterns were generically the same for all of chipmunk paths examined in this study. The data were compared to trends expected based on random or correlated random walks, as well as Lévy-walk models. The mean squared net displacement did not support the correlated random walk predictions, except at smaller spatial scales, but overall demonstrated Lévy-like super diffusive behaviour. Lévy-like patterns were also confirmed from the move-length distributions that demonstrated truncated-tail power-law behaviour. Although this would suggest invariance of the movement patterns at all spatial scales studied, fractal analysis revealed at least two transitions in movement patterns at scales of around 2 and 5 m. The transition point at 2 m was negatively correlated with the density of small trees, while the transition at ~5 m was positively correlated with the spatial distribution of large trees. As the habitat-preference data showed that small trees are among the least preferred habitat component, while large trees were among the most preferred habitat, chipmunks are likely to alter their movement behaviour to avoid small trees, and attracted towards large trees possibly to avoid predators. Overall, we determined three principal domains of movement: at smaller spatio-temporal scales, foraging activities dominate and the movement is highly correlated but also random;at intermediate spatial scales, chipmunks may be moving to avoid predators, using different environmental cues, and the movement is more directed (but still influenced by vegetation patterns at intermediate scales);at larger spatio-temporal scales, the movement is dominated by long-range/long-term memory and homing to burrows and other key habitat features, such as food caches, drives more directed movement. The fact that scale-dependent movement mechanisms could give rise to LW patterns is consistent with recent studies.展开更多
Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning ...Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].展开更多
基金sponsored partly by the National Key R&D Program of China (No. 2018YFC1406801)the National Natural Science Foundation of China (No. 41776185)the Key Course Construction Program of the Shanghai Municipal Education Commission (Biological Oceanography) (No. A1-0201-00-1204)
文摘Each type of fishery has its own characteristic behavior, and understanding this condition is an important part of devel- oping and managing fishing operations comprehensively. Based on the random walk model, the relationship between distance and frequency distribution of adjacent fishing positions was analyzed by the Commission for Conservation of Antarctic Marine Living Resources (CCAMLR) Subareas 48.1, 48.2, and 48.3. The frequency of distances between consecutive hauls demonstrated a heavy- tailed distribution, which could be used to estimate the value of parameter μ in the power function F(l)~ l μ of a random walk model to determine the type of random walk patterns that characterize Chinese krill fishery. Results indicated that the fishing pattern of the Chinese krill fishery is consistent with the Lévy random walk model, with which the step-length is applied to analyze the walking pattern. When a defined walk in a space of dimension is greater than one, the steps made are in isotropic random directions. Fur- thermore, a strong and positive correlation between fishing behavior (using the parameter μ as an indicator) and catch per unit effort of the Chinese krill fishery was observed.
基金Supported by the National Natural Science Foundation of China(11701319,11571198).
文摘The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.
基金supported by the National Natural Science Foundation of China (No. 10871177)the Ph. D.Programs Foundation of Ministry of Education of China (No. 20060335032)the Natural Science Foundation of Zhejiang Province of China (No. Y7080044)
文摘In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.
文摘The analysis of animal movement patterns can provide important information on animals’ responses to habitat features. In this study, the movement paths of eastern chipmunks (<em>Tamias striatus</em>) were examined in four landscapes, with different levels of habitat fragmentation, using either fluorescent powdering or spool-and-line tracking. Descriptions of the tree and ground vegetation communities were performed in the vicinity of the trail to obtain information on habitat use and habitat selection. Several key movement variables were calculated, including the total path length, net distance, fractal dimension, and radius of gyration. Despite statistically significant differences in some of the movement metrics between the four landscapes, the overall movement patterns were generically the same for all of chipmunk paths examined in this study. The data were compared to trends expected based on random or correlated random walks, as well as Lévy-walk models. The mean squared net displacement did not support the correlated random walk predictions, except at smaller spatial scales, but overall demonstrated Lévy-like super diffusive behaviour. Lévy-like patterns were also confirmed from the move-length distributions that demonstrated truncated-tail power-law behaviour. Although this would suggest invariance of the movement patterns at all spatial scales studied, fractal analysis revealed at least two transitions in movement patterns at scales of around 2 and 5 m. The transition point at 2 m was negatively correlated with the density of small trees, while the transition at ~5 m was positively correlated with the spatial distribution of large trees. As the habitat-preference data showed that small trees are among the least preferred habitat component, while large trees were among the most preferred habitat, chipmunks are likely to alter their movement behaviour to avoid small trees, and attracted towards large trees possibly to avoid predators. Overall, we determined three principal domains of movement: at smaller spatio-temporal scales, foraging activities dominate and the movement is highly correlated but also random;at intermediate spatial scales, chipmunks may be moving to avoid predators, using different environmental cues, and the movement is more directed (but still influenced by vegetation patterns at intermediate scales);at larger spatio-temporal scales, the movement is dominated by long-range/long-term memory and homing to burrows and other key habitat features, such as food caches, drives more directed movement. The fact that scale-dependent movement mechanisms could give rise to LW patterns is consistent with recent studies.
基金supported by NSFC(Grant No.11801075)supported by NSFC(Grant Nos.11671041,11531001 and 11371061)the Fundamental Research Funds for the Central Universities in UIBE(Grant No.16QN04)
文摘Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].
