Two-Sided First Exit Problem for Jump Diffusion Distribution Processes Having Jumps with a Mixture of Erlang

In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.

Poisson Process Modeling of Pure Jump Equities on the Ghana Stock Exchange

Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.

Upside and downside correlated jump risk premia of currency options and expected returns

This research explores upside and downside jumps in the dynamic processes of three rates:domestic interest rates,foreign interest rates,and exchange rates.To fill the gap between the asymmetric jump in the currency market and the current models,a correlated asymmetric jump model is proposed to capture the co-movement of the correlated jump risks for the three rates and identify the correlated jump risk premia.The likelihood ratio test results show that the new model performs best in 1-,3-,6-,and 12-month maturities.The in-and out-of-sample test results indicate that the new model can capture more risk factors with relatively small pricing errors.Finally,the risk factors captured by the new model can explain the exchange rate fluctuations for various economic events.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Alterable-element Method for Vehicle-bridge Interaction Considering the Transient Jump of Wheel

The so called "alterable-element method" (AEM) was introduced to deal with the coupling interac-tion of vehicle and sub-structure considering the actual transient jump of wheel, while the classical "contact all along" assumption based on which wheels and lower structure are always contact was abandoned. The alterable element used in this method is a conceptional element, which is used to calculate the coupling interaction of upper and lower structures and has some typical characteristics: firstly it flows along with the moving of contact point; secondly whether it is used for calculation depends on the contact state; thirdly its sizes could change according to specific problems and so on. VISUAL FORTRAN program was coded, and different moving vehicle models were presented taking into consideration the effects of random corrugation in the numerical study. The numerical solutions are favored comparing with the results obtained by alternative methods when there is no jump phenomenon existed. With abrupt irregularity, the transient jump of wheel was studied using the present method.

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is investigated in terms of the q-pair q(x)-q(x, A).

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

Arranging transient process used in iterative learning control system

Considering the same initial state error in each repetitive operation in the iterative learning system, a method of arranging the transient process is given. During the current iteration, the system will track the transient function firstly, and then the expected trajectory. After several iterations, the learning system output will trend to the arranged curve, which has avoided the effect of the initial error on the controller. Also the transient time can be changed as you need, which makes the designing simple and the operation easy. Then the detailed designing steps are given via the robot system. At last the simulation of the robot system is given, which shows the validity of the method.

A 1/3 PURE SUBHARMONIC SOLUTION AND TRANSIENT PROCESS FOR THE DUFFING'S EQUATION

The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.

Initial transient process in a simple helical flux compression generator

An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current density in the stator, is developed by means of a diffusion equation. A relationship between frequency of the conducting current, root of the characteristic function of Bessel equation and decay time in the armature is given. The skin depth in the helical stator is calculated and is compared with the approximate one which is widely used in the calculation of magnetic diffusion. Our analytical results are helpful to understanding the mechanism of the loss of magnetic flux in both the armature and stator and to suggesting an optimal design for improving performance of the helical flux compression generator.

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

Insiders' Hedging for Jump Diffusion Processes with Applications to Index Tracking

The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.

Effect of Carried-Envelope Phase on Transient Process in a Cascade-Type System

This paper investigates the effect of carried-envelope phase on transient process in a cascade-type atomic system, which is driven by two ultrashort laser pulses （probe and signal laser）. It is found that the one- and two-photon processes corresponding to pathway ｜0〉→｜1〉and ｜0〉→｜1〉→｜2〉 can be enhanced or ,suppressed by modulating the carried-envelope phases of probe laser pulse. Our numerical results also show that the transient populations of two excited states can be periodically affected by the carried-envelope phase of probe laser pulse. With certain time, the partial population transfer between two exited states can be realized just by adjusting the carried-envelope phase of probe laser pulse.

Poincaré Inequalities for Bounded Jump Processes

A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfying Poincaré inequality by using isoperimetric constants. It is λ0≥k0^2/（2R） and λ1 ≥k1^2/（2R）.

High-Accuracy Pneumatic Position Control by Applying Nonlinear Control and Arranging Transient Process

By applying a nonlinear control and arranging a transient process, the initiative error of the pneumatic servo positioning system is reduced largely, and a larger gain of the controller is used to improve the responding speed of the system at the same damping ratio. Therefore, a compromise is made among the responding speed, overshoot, robustness, adaptability and stability. In addition, a dynamic output feedback controller, including position velocity and acceleration （PVA） feedback, is designed to improve the performance of the system. And a nonlinear controller is reconstructed based on the linear output feedback controller to decrease noises and disturbances. The dynamic responses of the system are simulated and tested. Results show that the error is kept within 0.02 mm under different mass loads and the positioning transient process is smooth, without overshoot and speedy.

SYMMETRIC INTEGRAL AND CANONICAL EXTENSION FOR JUMP PROCESS SOME COMBINATORIAL RESULTS

Using approximation technique, we introduce the concepts of canonical extension and symmetrio integral for jump process and obtain some results in the chaotic form.

Temperature dependence of multi-jump magnetic switching process in epitaxial Fe/MgO(001) films

Temperature dependence of magnetic switching processes with multiple jumps in Fe/MgO（001） films is investigated by magnetoresistance measurements. When the temperature decreases from 300K to 80K, the measured three-jump hysteresis loops turn into two-jump loops. The temperature dependence of the fourfold in-plane magnetic anisotropy constant K1, domain wall pinning energy, and an additional uniaxial magnetic anisotropy constant KUare responsible for this transformation. The strengths of K1 and domain wall pinning energy increase with decreasing temperature, but KU remains unchanged. Moreover, magnetization reversal mechanisms, with either two successive or two separate 90°domain wall propagation, are introduced to explain the multi-jump magnetic switching process in epitaxial Fe/MgO（001） films at different temperatures.

Optimal Control for Insurers with a Jump-diffusion Risk Process

In this paper, the optimal XL-reinsurance of an insurer with jump-diffusion risk process is studied. With the assumptions that the risk process is a compound Possion process perturbed by a standard Brownian motion and the reinsurance premium is calculated according to the variance principle, the implicit expression of the priority and corresponding value function when the utility function is exponential are obtained. At last, the value function is argued, the properties of the priority about parameters are discussed and numerical results of the priority for various claim-size distributions are shown.