激光陀螺随机噪声参数估计和滤波方法研究

激光陀螺(RLG)中随机噪声是影响其精度的一个重要因素,针对其噪声的特殊性质,采用小波方法去除随机噪声,提高激光陀螺的精度。通过小波分析的参数估计方法获得噪声参数,并用小波阈值滤波方法去除噪声,对某型号的RLG的滤波结果表明了该方法的有效性。     

A stochastic maximum principle for systems with jumps, with applications to finance

We consider a stochastic control problem with linear dynamics with jumps, convex cost criterion, and convex state constraint, in which the control enters the drift, the diffusion, and the jump coefficients. We allow these coefficients to be random, and do not impose any L^p-bounds on the control.

We obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality. This is the first version of the stochastic maximum principle that covers the consumption–investment problem in which there are jumps in the price system.     

Modelling of the substrate heterogeneities experienced by a limited microbial population in scale-down and in large-scale bioreactors

A methodology based on stochastic modelling is presented to describe the influence of the bioreactor heterogeneity on the microorganisms growth and physiology. The stochastic model is composed of two sub-models: a microorganism circulation sub-model and a fluid mixing sub-model used for the characterization of the concentration gradient. The first one is expressed by a classical stochastic model (with random number generation), whereas the second one is expressed by a stochastic Markov chain. Their superimposition permits to obtain the concentration profiles experienced by the microorganisms in the bioreactor. The simulation results are expressed in the form of frequency distributions. At first, the study has been focused on the design of scale-down reactors (SDR). This kind of reactor has been reported to be an efficient tool to study at a small-scale the hydrodynamic behaviour encountered in large-scale reactor [P. Neubauer, L. Horvat, S.O. Enfors, Influence of substrate oscillations on acetate formation and growth yield in Escherichia coli glucose limited fed-batch cultivations, Biotechnol. Bioeng. 47 (1995) 139–146]. Several parameters affecting the shape of the frequency distributions have been tested. Among these, it appears that the perturbation frequency, the exposure time and the design of the non-mixed part of the SDR have a significant influence on the shape of the distributions. The respective influence of all these parameters must be taken into account in order to obtain representative results. As a general trend, the increase of the recirculation flow rate between the mixed and the non-mixed part of the SDR induce a shift of the frequency distribution for the lower relative concentrations, which suggests an attenuation of the scale-down effect. This has been validated by using the SDR in the case of the cultivation of Saccharomyces cerevisiae. However, the influence of the non-mixed part of the SDR is not quite well understood if only taking account of the frequency distribution analysis, and supplementary experiments are required to elucidate the underlying mechanism.

The aspect of the frequency distributions suggests that both the design and the operating conditions of a scale-down reactor need to be adjusted in order to match the behaviour of a given large-scale reactor. Examples of frequency distributions obtained in the case of large-scale reactors are given.     

Danckwerts’ law for mean residence time revisited

This paper shows that Danckwerts’ law for mean residence time in a vessel with continuous and steady throughflow holds for a stochastic model based on a Markov chain for the particle spatial position, under a set of three very general conditions on the transfer probabilities. These are natural conditions and represent mass balance conditions on the transfer between spatial regions in the process. It is shown that a stochastic model for particle residence time distribution with these three conditions may describe almost any physical flow configuration, and also covers published mathematical RTD models, independent of their mathematical form or the nature of the associated boundary conditions, models for which Danckwert's law has hitherto been shown to be satisfied on a case-by-case basis. Two examples, namely those birth-death Markov chains and fluidized bed models are discussed.     

Equivalent stochastic control problems

A decentralized stochastic control problem is called static if the observations available for any one decision do not depend on the other decisions. Otherwise it is called dynamic. We consider only problems with a finite number of decisions. A notion of equivalence between problems, suitable for complexity analysis, is defined. It turns out that a large class of dynamic problems can be reduced to equivalent static problems. The class includes all sequential discrete variable problems and some of the most studied continuous variable problems.     

Controlling the losing probability in a monotone game

We deal with a complex game between Alice and Bob where each contender’s probability of victory grows monotonically by unknown amounts with the resources employed. For a fixed effort on Alice’s part, Bob increases his resources on the basis of the results for each round (victory, tie or defeat) with the aim of reducing the probability of defeat to below a given threshold. We read this goal in terms of computing a confidence interval for the probability of losing and realize that the moves in some contests may bring in an indeterminacy trap: in certain games Bob cannot simultaneously have both a low probability-of-defeat measure and a narrow confidence interval. We use the inferential mechanism called twisting argument to compute the above interval on the basis of two joint statistics. Careful use of such statistics allows us to avoid indeterminacy.     

Simulation-based sequential analysis of Markov switching stochastic volatility models

We propose a simulation-based algorithm for inference in stochastic volatility models with possible regime switching in which the regime state is governed by a first-order Markov process. Using auxiliary particle filters we developed a strategy to sequentially learn about states and parameters of the model. The methodology is tested against a synthetic time series and validated with a real financial time series: the IBOVESPA stock index (São Paulo Stock Exchange).     

Decision support in early development phases—A case study from machine engineering

In the case study presented in this paper we consider early development phases of a mechanical product. We want to evaluate different concepts and decide which one(s) to pursue. A problem in early phases is that usually no test runs are available. In our case study, based on a standard, there are ways to compute the lifetime distributions of the components of the different concepts. Some parameters needed for these computations are not known precisely. Unfortunately, the lifetime distributions of the components are highly sensitive to these parameters. Our approach is to equip these parameters with distributions. These distributions would be called prior distributions in Bayesian terminology, but no update is possible since no test runs are available. Our approach implies that the distribution of the system lifetime for each concept is random, i.e. we get random elements in the space of lifetime distributions. Using Monte-Carlo simulations, we demonstrate several ways to compare the random lifetime distributions of the concepts. Some of these comparisons use stochastic orderings. We also introduce a new stochastic ordering which is particularly suitable for reliability purposes. Our case study, consisting of three scenarios, allows us to demonstrate some conclusions that can be reached.     

Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

A ‘proportional’ order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the ‘full-state’ policy is derived. The comparison between the two policies demonstrates that the ‘intuitively’ designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects.