Moderate Deviations for Marked Hawkes Processes

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.

Limit Theorems for Inverse Process Tn of Hawkes Process

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

Rough Heston Models with Variable Vol-of-Vol and Option Pricing

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.

Topology tracking of dynamic UAV wireless networks

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.