The joint Laplace transforms for killed diffusion occupation times

The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.

A Joint Laplace Transform for Pre-exit Diffusion of Occupation Times

For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.

OCCUPATION TIMES OF BALLS BY BROWNIAN MOTION WITH DRIFT

Let X = {Xt,t >=0} be a d-dimensional (d>= 2) standard Brownian motion with drift c started at a fixed x, and BR = {x E Rd: |x| < R}, the ball centered at 0 with radius R. Consider the distributions of TR(t) and TR(∞), where TR(t) denotes the time spent by X in BR up to time t and TR(∞) the total time of X spent in BR. Explicit formulas for the Laplace transform of TR(∞) and the double Laplace transform of TR(t) are obtained.

On States of Total Weighted Occupation Times for Superdiffusions

Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.

Analysis of occupation time of vehicles at urban unsignalized intersections in non-lane-based mixed traffic conditions

In India, traffic flow on roads is highly mixed in nature with wide variations in the static and dynamic characteristics of vehicles. At unsignalized intersections, vehicles generally do not follow lane discipline and ignore the rules of priority. Drivers generally become more aggressive and tend to cross the uncontrolled intersections without considering the conflicting traffic. All these conditions cause a very complex traffic situation at unsignal- ized intersections which have a great impact on the capacity and performance of traffic intersections. A new method called additive conflict flow （ACF） method is suitable to determine the capacity of unsignalized inter- sections in non-lane-based mixed traffic conditions as prevailing in India. Occupation time is the key parameter for ACF method, which is defined as the time spent by a vehicle in the conflict area at the intersection. Data for this study were collected at two three-legged unsignalized intersections （one is uncontrolled and other one is semi- controlled） in Mangalore city, India using video-graphic technique during peak periods on three consecutive week days. The occupation time of vehicles at these intersections were studied and compared. The data on conflicting traffic volume and occupation time by each subject vehicle at the conflict area were extracted from the videos using image processing software. The subject vehicles were divided into three categories： two wheelers,cars, and auto-rickshaws. Mathematical relationships were developed to relate the occupation time of different cate- gories of vehicles with the conflicting flow of vehicles for various movements at both the intersections. It was found that occupation time increases with the increasing con- flicting traffic and observed to be higher at the uncontrolled intersection compared to the semicontrolled intersec- tion. The segregated turning movements and the presence of mini roundabout at the semicontrolled intersection reduces the conflicts of vehicular movements, which ulti- mately reduces the occupation time. The proposed methodology will be useful to determine the occupation time for various movements at unsignalized intersections. The models developed in the study can be used by practitioners and traffic engineers to estimate the capacity of unsignalized intersections in non-lane-based discipline and mixed traffic conditions.

ABSOLUTE CONTINUITY OF THE OCCUPATION TIME PROCESSES WITH RESPECT TO LEBESGUE MEASURE FOR SUPER－BROWNIAN MOTION

Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d≤3) when the initial measure of the Super-Brownian motion has the absolute continuity.

CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).

Some Properties of Conditioned Superdiffusion

Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.

Rising Women's Occupations in Modern Times

IN traditional Chinese society, having an occupation, as a means of making a living, was the "privilege" of women at lower levels of society. Married and unmarried women who had servants were sneered at if they had an occupation. The work that lower class women did was generally related to production and labor, market exchange, communications

Handover Traffic Model and Channel Occupancy Time in LEO Satellite Networks

This paper presents a method of determining handover traffic and mean channel occu-pancy time of a traffic model for the LEO(Low Earth Orbit)satellite networks.The mainideas are that the handover traffic is mainly due to the movement of the satellite and that thevelocity of the mobile terminals and earth rotation are ignored.The performance level can becalculated according to different handover queuing models.

Diffusion occupation time before exiting

Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.

An occupation time related potential measure for diffusion processes

In this paper, for homogeneous diffusion processes, the approach of Y. Li and X. Zhou [Statist. Probab. Lett., 2014, 94： 48-55] is adopted to find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals （-∞, a） and （a, ∞）. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions for Brownian motion with drift, skew Brownian motion, and Brownian motion with two-valued drift, respectively.

Regularity of the Density for the Total Weighted Occupation Measure of Super-Brownain Motion

Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

A large deviation for occupation time of critical branching α-stable process

In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations. Our result is an extension of Cox and Griffeath’s (in 1985) for branching Brownian motion for d > 4.

OCCUPATION TIME PROCESSES OF FLEMING-VIOT PROCESSES

Suppose that Xt is the Fleming-Viot process associated with fractional power Laplacian operator -(-△)α/2 0 < α≥ 2, and Yt= f_0￣t Xs.ds is the so-called occupation time process.In this paper) the asymptotic behavior at a large time and the absolute continuity of Yt are investigated.

Functional central limit theorem for super α-stable processes

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.