Particle systems on flows

We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process.     

一类过程摄动系统的无阻塞鲁棒性

使用参数Dioid模块网络法,把含大量摄动参数的在普通极大代数意义下非线性状态空间模型在参数Dioid意义下线性化,在此基础上研究一类过程摄动系统的无阻塞鲁棒性.给出了有限缓冲串行生产系统在没有缓冲器下无阻塞的充要条件和充分条件.     

Equivariant mappings: a new approach in stochastic simulations

Stochastic simulations on manifolds usually are traced back to ⁿ via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry.     

模糊数序列的收敛性

探讨L-R型模糊数序列的S-和问题，定义关于模糊数的模糊小于的概念，在此基础上探讨模糊数的有序性，模糊数的截集函数的连续性，模糊数的格结构以及模糊数序列的收敛性等重要性质。     

Subgame Consistent Cooperative Solutions in Stochastic Differential Games

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

Bounding multi-stage stochastic programs from above

The purpose of this paper is to present general approaches for bounding some multi-stage stochastic programs from above. The results are based on restricting the solution set, such that the remaining multi-stage stochastic program is easy to solve. An example where the methods can be applied is presented.Supported in part by NATO Collaborative Research Grant No. 0785/87.     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.     

Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Range reliability in random walks

This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is denned as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic.