Temporal Point Processes(TPPs),especially the Hawkes process,are commonly used for modeling asynchronous event-type big data,such as financial transactions and user behaviors in social networks.Due to the strong fitti...Temporal Point Processes(TPPs),especially the Hawkes process,are commonly used for modeling asynchronous event-type big data,such as financial transactions and user behaviors in social networks.Due to the strong fitting ability of neural networks,various neural point processes are proposed,among which the neural Hawkes processes based on self-attention,such as the Transformer Hawkes Process(THP),achieve distinct performance improvement.Although the THP has gained popular applications,it still suffers from low accuracy and unstable performance in sequence prediction tasks when training on history sequences and inferencing about the future,which is a prevalent paradigm in realistic sequence analysis.Conventional THP and its variants generally adopt sinusoid embedding in transformers,which also shows severe performance sensitivity to temporal change or noise by empirical study.To deal with the above problems,we propose a new Rotary position embedding-based THP(RoTHP),which for the first time encodes the temporal information in the Hawkes process with rotary embedding,and then constructs the intensity function adaptively.Notably,we show the translation invariance property of the RoTHP induced by the relative time encoding when coupled with the Hawkes process theoretically,and illustrate its sequence prediction flexibility.Extensive experiments are conducted,which demonstrate that the proposed RoTHP can be better generalized when dealing with sequence data with timestamp translations or noise,and show its superior performance in sequence prediction tasks.展开更多
Previous research has mainly focused on risk models constructed from Markov processes.This article is an extension of the risk model based on Hawkes’variable memory process with a partial dividend payment strategy to...Previous research has mainly focused on risk models constructed from Markov processes.This article is an extension of the risk model based on Hawkes’variable memory process with a partial dividend payment strategy to shareholders,a constant threshold b,and a dependence between the amounts of claims and the inter-claim times via the Spearman copula.We study the probability of ultimate ruin associated with this risk model and conduct simulations to observe the behavior of this probability.展开更多
We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawk...We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.展开更多
We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked...We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.展开更多
We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate t...We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn展开更多
Wireless network is the communication foundation that supports the intelligentization of Unmanned Aerial Vehicle(UAV) swarm. The topology of UAV communication network is the key to understanding and analyzing the beha...Wireless network is the communication foundation that supports the intelligentization of Unmanned Aerial Vehicle(UAV) swarm. The topology of UAV communication network is the key to understanding and analyzing the behavior of UAV swarm, thus supporting the further prediction of UAV operations. However, the UAV swarm network topology varies over time due to the high mobility and diversified mission requirements of UAVs. Therefore, it is important but challenging to research dynamic topology inference for tracking the topology changes of the UAV network,especially in non-cooperative manner. In this paper, we study the problem of inferring UAV swarm network topology based on external observations, and propose a dynamic topology inference method. First, we establish a sensing framework for acquiring the communication behavior of the target network over time. Then, we expand the multi-dimensional dynamic Hawkes process to model the communication event sequence in a dynamic wireless network. Finally, combining the sliding time window mechanism, the maximum weighted likelihood estimation is applied to inferring the network topology. Extensive simulation results demonstrate the effectiveness of the proposed method.展开更多
In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional ...In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.展开更多
基金supported by the Shenzhen Science and Technology Program(No.RCBS20221008093331068).
文摘Temporal Point Processes(TPPs),especially the Hawkes process,are commonly used for modeling asynchronous event-type big data,such as financial transactions and user behaviors in social networks.Due to the strong fitting ability of neural networks,various neural point processes are proposed,among which the neural Hawkes processes based on self-attention,such as the Transformer Hawkes Process(THP),achieve distinct performance improvement.Although the THP has gained popular applications,it still suffers from low accuracy and unstable performance in sequence prediction tasks when training on history sequences and inferencing about the future,which is a prevalent paradigm in realistic sequence analysis.Conventional THP and its variants generally adopt sinusoid embedding in transformers,which also shows severe performance sensitivity to temporal change or noise by empirical study.To deal with the above problems,we propose a new Rotary position embedding-based THP(RoTHP),which for the first time encodes the temporal information in the Hawkes process with rotary embedding,and then constructs the intensity function adaptively.Notably,we show the translation invariance property of the RoTHP induced by the relative time encoding when coupled with the Hawkes process theoretically,and illustrate its sequence prediction flexibility.Extensive experiments are conducted,which demonstrate that the proposed RoTHP can be better generalized when dealing with sequence data with timestamp translations or noise,and show its superior performance in sequence prediction tasks.
文摘Previous research has mainly focused on risk models constructed from Markov processes.This article is an extension of the risk model based on Hawkes’variable memory process with a partial dividend payment strategy to shareholders,a constant threshold b,and a dependence between the amounts of claims and the inter-claim times via the Spearman copula.We study the probability of ultimate ruin associated with this risk model and conduct simulations to observe the behavior of this probability.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(No.102/01003002031)Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(No.215/20506341 and No.215/20506277).
文摘We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.
文摘We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.
文摘We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn
基金supported by the National Natural Science Foundation of China(Nos.U20B2038,61871398,61901520 and 61931011)the Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province,China(No.BK20190030)。
文摘Wireless network is the communication foundation that supports the intelligentization of Unmanned Aerial Vehicle(UAV) swarm. The topology of UAV communication network is the key to understanding and analyzing the behavior of UAV swarm, thus supporting the further prediction of UAV operations. However, the UAV swarm network topology varies over time due to the high mobility and diversified mission requirements of UAVs. Therefore, it is important but challenging to research dynamic topology inference for tracking the topology changes of the UAV network,especially in non-cooperative manner. In this paper, we study the problem of inferring UAV swarm network topology based on external observations, and propose a dynamic topology inference method. First, we establish a sensing framework for acquiring the communication behavior of the target network over time. Then, we expand the multi-dimensional dynamic Hawkes process to model the communication event sequence in a dynamic wireless network. Finally, combining the sliding time window mechanism, the maximum weighted likelihood estimation is applied to inferring the network topology. Extensive simulation results demonstrate the effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China (No. 12171 122)Shenzhen Science and Technology Program (No. RCJC20210609103755110)+1 种基金Fundamental Research Project of Shenzhen (No. JCYJ20190806143201649)supported by National Natural Science Foundation of China (Grant No. 12071373).
文摘In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.
