A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure

We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals.     

带ARMA(1,1)条件异方差相关的随机波动模型的MCMC算法

我们首先提出了一个带ARMA(1,1)条件异方差相关的随机波动模型,它是基本的随机波动模型的一个自然的推广.进一步,对于这一新模型,我们给出了一个马尔可夫链蒙特卡罗(M CM C)算法.最后,利用该模型的模拟数据,展示了M CM C算法在这种模型中的应用.     

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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.     

Physical Analysis of a Possibility to Reach the 1.30-μm Emission from the GaAs-Based VCSELs with the InGaAs/GaAs Quantum-Well Active Regions and the Intentionally Detuned Optical Cavities

Physical aspects of an operation of the GaAs-based InGaAs/GaAs quantum-well (QW) VCSELs with the intentionally detuned optical cavities have been considered in the present paper using the comprehensive three-dimensional self-consistent optical–electrical–thermal-gain simulation. In GaAs-based structures, very good DBR resonator mirrors and a very efficient methods to confine radially both the current spreading and the electromagnetic field with the aid of oxide apertures may be applied. It has been found using the above simulation that even currently available immature technology enables manufacturing the above devices emitting radiation of wavelengths over 1.20 μm. In particular, while the room-temperature 1.30-μm lasing emission is still beyond possibilities of the InGaAs/GaAs QW VCSELs, these structures may offer analogous 1.25-μm emission, especially for the high-power and/or high-temperature operation.     

Learning Markov chains in fractal compression of image data

In a recent paper [17] we proposed a stochastic algorithm which generates optimal probabilities for the decompression of an image represented by the fixed point of an IFS system (SAOP). We show here that such an algorithm is in fact a non trivial example of Generalized Random System with Complete Connections. We also exhibit a generalization which could represent the solution to the inverse problem for an image with grey levels, if a fixed set of contraction maps is available. Received: 1 July 2002     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Stochastic modelling of reservoir operations

The nature of hydrologic parameters in reservoir management models is uncertain. In mathematical programming models the uncertainties are dealt with either indirectly (sensitivity analysis of a deterministic model) or directly by applying a chance-constrained type of formulation or some of the stochastic programming techniques (LP and DP based models). Various approaches are reviewed in the paper. Moran's theory of storage is an alternative stochastic modelling approach to mathematical programming techniques. The basis of the approach and its application is presented. Reliability programming is a stochastic technique based on the chance-constrained approach, where the reliabilities of the chance constraints are considered as extra decision variables in the model. The problem of random event treatment in the reservoir management model formulation using reliability programming is addressed in this paper.     

Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.