广义单瞬时生-灭过程的Kendall猜想

A new structure with the special property that instantaneous state and catastrophes is imposed to ordinary birth-death processes is considered. Kendall's conjecture for the processes is proved to be right.     

ON COUPLING OF JUMP PROCESSES

This is a sequel to the paper [3] in which the marginality, regularity and orderpreservation for couplings of jump processes are studied. The main purpose of this note is to present a criterion and some practical suffcient conditions for the success of couplings and some criteria for the monotonicity of jump processes.     

$L^2$-Algebraic Decay Rate for Transient Birth-Death Processes

This paper is a continuation of the study of the algebraic speed for Markov processes.The authors concentrate on algebraic decay rate for the transient birth-death processes.According to the classifica...     

ERGODIC THEOREMS FOR LINEAR GROWTH PROCESSES WITH DIFFUSION

In this paper a simple class of the infinite dimensional reaction-diffusion processes——the linear growth processes with diffusion is studied. This paper is devoted to the ergodicity of these processes. Tne exact value of parameters at which the change of phase occurs is given, the set of all translation invariant invariant measures and the corresponding domain of attraction for each translation invariant invariant measure are described.     

Talagrand Inequality on Free Path Space and Application to Stochastic Reaction Diffusion Equations

By using a split argument due to[1],the transportation cost inequality is established on the free path space of Markov processes.The general result is applied to stochastic reaction diffusion equations with random initial values.     

Successful couplings for difusion processes with state-dependent switching

This work is concerned with successful couplings for a class of multidimensional difusion processes with state-dependent switching.We construct a type of couplings for this class of processes,and give some sufcient conditions to guarantee this type of couplings to be successful.Besides,two illustrative examples are provided.     

Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks

Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ψ. The goal of the paper is to give bounds on the amplitude max ψ/ min ψ. Two approaches are proposed: One using a path method and the other one, restricted to the reversible situation, based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for which infinity is an entrance boundary. The interest of estimating the ratio is the reduction of the quantitative study of convergence to quasi-stationarity to the convergence to equilibrium of related ergodic processes, as seen by Diaconis and Miclo(2014).     

不变测度,比例极限和Martin边界

In this article the notion of quasi-symmetry is introduced. It is proved that the quasisymmetry is equivalent to the uniqueness of invariant measure of Levy processes in some senseMoreover,the relationship between ratio limits and invariant measures is studied.     

Ruin probabilities for a risk model with two classes of claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.     

Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the...     

POTENTIALITY AND REVERSIBILITY FOR THE N-SPIN-FLIP PROCESSES AND THE N-GENERALIZED SPIN-FLIP-PROCESSES

The Markov processes with infinite particle system are one of the new branches in probability, recently it is developed rapidly. It relates not only to the statistical physics of balanced state, but also to the statistical physics of the unbalanced state and other subjectst In this paper, two kinds of Markov processes with infinite     

Limiting process of absorbing Markov chains

We outline an approach to investigate the limiting law of an absorbing Markov chain conditional on having not been absorbed for long time. The main idea is to employ Donsker-Varadhan＇s entropy functional which is typically used as the large deviation rate function for Markov processes. This approach provides an interpretation for a certain quasi-ergodicity     

Successful couplings for a class of stochastic differential equations driven by Lvy processes

By constructing proper coupling operators for the integro-differential type Markov generator,we establish the existence of a successful coupling for a class of stochastic differential equations driven by L’evy processes.Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups,and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable L’evy processes.     

First passage models for denumerable semi-Markov decision processes with nonnegative discounted costs

This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs.The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set.We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy.Then,we prove that the value function satisfies the optimality equation and there exists an optimal(or e-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach.Further we give some properties of optimal policies.In addition,a value iteration algorithm for computing the value function and optimal policies is developed and an example is given.Finally,it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.     

Parametric estimation of discretely sampled Gamma-OU processes

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.     

Generalized Green Correspondence of Graded Modules

The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.     

ON THE CONVERGENCE FOR NULL-ARRAYS OF THE POINT PROCESSES

The purpose of this paper is first to establish a representation of the Laplace transformfor the regular infinitely divisible point processes,and then to give a sufficient and neccesarycondition for convergence of the null-arrays toward a regular infinitely divisible pointprocess.     

A Filtration of Wick Algebra and Its Application to Quantum SDEs

A family of closed snbalgebras, indexed by R(the set of real numbers), of the Wick algebra is constructed. Fundamental properties of tile family are shown including the increasing property and the right-continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators.     

ON THE RUIN FUNCTIONS FOR A CORRELATED AGGREGATE CLAIMS MODEL WITH POISSON AND ERLANG RISK PROCESSES

This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.     

LAPLACE TRANSFORM OF THE SURVIVAL PROBABILITY UNDER SPARRE ANDERSEN MODEL

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.