Invariant measures for the strong-facilitated exclusion process

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will...     

THE SET OF THE INVARIANT MEASURES OF BOUNDED SPIN-FLIP PROCESSES WITH POTENTIAL

In this paper, some properties of the invariant measures of bounded spin-flip processes are discussed. It is proved that all invariant measures of a bounded spinflip process with potential are reversible measures if its speed functions have locally finite range interaction. Therefore, all invariant measures of the process are the Gibbs states of the potential. It is also proved that for each given potential, there exists a spin-flip process suth that all of its invariant measures are the Gibbs states of the potential.     

WEAKLY ALMOST PERIODIC POINT AND ERGODIC MEASURE

Let X be a compact metric space and f: X→X be continuous.This pape introduces the notion of weakly almost periodic point, which is a generalization of the notion of almost periodic point, proves that each of f-invariant ergodic measures can be generated by a weakly almost periodic point of f and gives some equivalent conditions for that f has an invariant ergodic measure whose support is X and ones for that f has no non-atomic invariant ergodic measure, the latter is a generalization of the Blokh's work on self-maps of the interval. Also two formulae for calculating the togological entropy are obtained.     

Some ergodic theorems for a parabolic Anderson model

In this paper,we study some ergodic theorems of a class of linear systems of interacting diffusions,which is a parabolic Anderson model.First,under the assumption that the transition kernel a=(a(i,j)) i,j∈s is doubly stochastic,we obtain the long-time convergence to an invariant probability measure νh starting from a bounded a-harmonic function h based on self-duality property,and then we show the convergence to the invariant probability measure νh holds for a broad class of initial distributions.Second,if(a(i,j)) i,j∈S is transient and symmetric,and the diffusion parameter c remains below a threshold,we are able to determine the set of extremal invariant probability measures with finite second moment.Finally,in the case that the transition kernel(a(i,j)) i,j∈S is doubly stochastic and satisfies Case I(see Case I in [Shiga,T.:An interacting system in population genetics.J.Math.Kyoto Univ.,20,213-242(1980)]),we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.     

Compound Binomial Risk Model with Random Income in Markov Chain Environment北大核心CSCD

In this paper, I consider that the actuarial model is affected by the environmental process Θ, premium income counting process η, claim counting process I and the claim process B, and establish a compound binomial risk model with random income in Markov chain environment, which is called MRICM, for short. The characteristic five-tuple set is given. It is proved that there exists a probabilistic space (Ω, F, P), and MRICM(Θ, η, I, B) defined on it, and its characteristic five-tuple set coincides with the given one. The recursive equations of conditional ruin probability for finite time and infinite time are obtained. © 2022 Chinese Academy of Sciences. All rights reserved.     

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.     

Invariant sets and solutions to the generalized thin film equation

The invariant sets and the solutions of the 1 2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set E0 = {u : ux = vxF(u), uy = vyF(u)}, where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the l l-dimensional nonlinear evolution equations.     

Decay parameter and related properties of n-type branching processes

We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching processes and 2-type Markov branching processes. Investigating such behavior is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for n-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Zn+ \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC -invariant measures/vectors and quasi-distributions of such processes are deeply considered. λC -invariant measures and quasi-stationary distributions for the process on C are presented.     

On quasi-weakly almost periodic points

The core problem of dynamical systems is to study the asymptotic behaviors of orbits and their topological structures. It is well known that the orbits with certain recurrence and generating ergodic (or invariant) measures are important, such orbits form a full measure set for all invariant measures of the system, its closure is called the measure center of the system. To investigate this set, Zhou introduced the notions of weakly almost periodic point and quasi-weakly almost periodic point in 1990s, and presented some open problems on complexity of discrete dynamical systems in 2004. One of the open problems is as follows: for a quasi-weakly almost periodic point but not weakly almost periodic, is there an invariant measure generated by its orbit such that the support of this measure is equal to its minimal center of attraction (a closed invariant set which attracts its orbit statistically for every point and has no proper subset with this property)? Up to now, the problem remains open. In this paper, we construct two points in the one-sided shift system of two symbols, each of them generates a sub-shift system. One gives a positive answer to the question above, the other answers in the negative. Thus we solve the open problem completely. More important, the two examples show that a proper quasi-weakly almost periodic orbit behaves very differently with weakly almost periodic orbit.     

Option Pricing for Time-Change Exponential Levy Model Under Memm

The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Levy process. European option pricing formula is obtained under the minimal entropy martingale measure （MEMM） and applied to several examples of particular time-change Levy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.