带移民的马尔可夫分支过程的唯一性

本文考虑了一类带移民的马尔可夫分支过程,给出了这个过程的唯一性和正则性的判定准则。     

Uniqueness and Extinction of Weighted Markov Branching Processes

This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80     

The Maximum of a Critical Branching Wiener Process

Consider a critical branching Wiener process on ¹. Let M(n) be the location of the most right particle at time n. A limit distribution theorem is proved for n ^–1/2 M(n).     

A Decomposition of Markov Processes via Group Actions

We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal to orbits) and an angular part (along an orbit). We show that given a radial path, the conditioned angular part is a nonhomogeneous Lévy process in a homogeneous space, we obtain a representation of such processes and, as a consequence, we extend the well-known skew-product of Euclidean Brownian motion to a general setting.      

Approximation of quantum Lévy processes by quantum random walks

Every quantum Lévy process with a bounded stochastic generator is shown to arise as a strong limit of a family of suitably scaled quantum random walks.     

Asymptotic expansion for forward-backward SDEs with jumps

This work provides a semi-analytic approximation method for decoupled forward-backward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit of the forward SDE. We provide a semi-analytic solution technique as well as its error estimate for which we only need to solve essentially a system of linear ODEs. In the case of a finite jump measure with a bounded intensity, the method can also handle state-dependent and hence non-Poissonian jumps, which are quite relevant for many practical applications.     

On Entire Moments of Self-Similar Markov Processes

We consider a risk-based asset allocation problem in a Markov, regime-switching, pure jump model. With a convex risk measure of the terminal wealth of an investor as a proxy for risk, we formulate the risk-based asset allocation problem as a zero-sum, two-person, stochastic differential game between the investor and the market. The HJB dynamic programming approach is used to discuss the game problem. A semi-analytical solution of the game problem is obtained in a particular case.     

带再生的碰撞分枝过程的吸收概率

本文研究了带再生的碰撞分枝过程,得到了两种情况下吸收概率的表达式.     

Pricing and hedging of variable annuities with state-dependent fees

We investigate the problem of pricing and hedging variable annuity contracts for which the fee deducted from the policyholder’s account depends on the account value. It is believed that state-dependent fees are beneficial to policyholders and insurers since they reduce policyholders’ incentives to lapse the policies and match the costs incurred by policyholders with the pay-offs received from embedded guarantees. We consider an incomplete financial market which consists of two risky assets modelled with a two-dimensional Lévy process. One of the assets is a security which can be traded by the insurer, and the second asset is a security which is the underlying fund for the variable annuity contract. In our model we derive an equation from which the fee for the guaranteed benefit can be calculated and we characterize a strategy which allows the insurer to hedge the benefit. To solve the pricing and hedging problem in an incomplete financial market we apply a quadratic objective.     

Feller Property and Infinitesimal Generator of the Exploration Process

We consider the exploration process associated to the continuous random tree (CRT) built using a Lévy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale. The research of the second author was partially supported by NSERC Discovery Grants of the Probability group at Univ. of British Columbia.     

A Critical Branching Process with Stationary-Limiting Distribution

Abstract

Seneta (Seneta, E. The stationary distribution of a branching process allowing immigration: A remark on the critical case. J. Royal Statistical Society, Series B 1968, 30, 176–179) shows that a critical branching process with pure immigration has a stationary-limiting distribution provided that its offspring variance is infinite. We obtain a stationary-limiting distribution keeping the variance finite but allowing an emigration–immigration component in each generation.     

Lévy noise perturbation for an epidemic model with impact of media coverage

ABSTRACT

This work is devoted to study the existence and uniqueness of global positive solution for a stochastic epidemic model with media coverage driven by Lévy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Numerical simulations are presented to confirm the theoretical results.     

The explicit chaotic representation of the powers of increments of Lévy processes

This paper presents a computationally explicit formula of the chaotic representation property (CRP) for the powers of increments of a Lévy process. The formula can be used to obtain the integrands of the CRP in terms of orthogonal compensated power jump processes and the CRP in terms of Poisson random measures. Simulation results demonstrate that the performance of the representation is satisfactory. The CRP of a number of financial derivatives can be found by expressing them in terms of the powers of increments of the underlying Lévy process using Taylor's expansion.     

多维指数族分布的参数线性容许估计的一个充分条件

本文利用唯一的Ｂａｙｅｓ估计是容许估计的原理,构造了一个先验分布π１（θ）＝Ｍβ－１（θ）ψ（θ）ｅｘｐ∑ｎｉ＝１∫θｉθｉ０ｂ－ｒｉ（ｔ）ａｉｎｄｔｉ,当它满足一定的条件时,证明了在均方损失下,多维指数族分布ｆθ（ｘ）＝β（θ）ｅｘｐθ′ｘ的参数ｒ（θ）的唯一Ｂａｙｅｓ估计为线性函数ａ′ｘ＋ｂ,因而也是容许估计     

Extinction time and the total mass of the continuous-state branching processes with competition

Consider a general continuous-state branching process with additional interaction, which destroys the branching property. We give precise conditions on the interaction term, in order to decide whether the extinction time of the process remains or not bounded as the initial value tends to infinity, and similarly for the total mass of the process.     

独立同分布随机环境中两性Galton-Watson分支过程灭绝概率的渐近行为

本文研究了独立同分布随机环境中的两性Galton-Watson分支过程,在上临界情形下,当k充分大时,qk≤ck<'-α>.