scholarly journals Forward sensitivity analysis for contracting stochastic systems

2018 ◽  
Vol 50 (01) ◽  
pp. 102-130
Author(s):  
Thomas Flynn
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Systems ◽  
Wasserstein Distance ◽  
Gradient Estimation ◽  
Deterministic Systems ◽  
Continuous State Space ◽  
Continuous State ◽  
Sensitivity Analysis Method ◽  
One Step ◽  
The One

Abstract In this paper we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee differentiability of stationary costs. Then we show how to estimate the derivatives, deriving an estimator that can be seen as a generalization of the forward sensitivity analysis method used in deterministic systems. We apply the results to examples, including a neural network model.

scholarly journals pth Mean Practical Stability for Large-Scale Itô Stochastic Systems with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Yun ◽  
Huisheng Shu ◽  
Yan Che
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Practical Stability ◽  
Nonlinear Stochastic Systems ◽  
Deterministic Systems ◽  
The One

Motivated by the study of a class of large-scale stochastic systems with Markovian switching, this correspondence paper is concerned with the practical stability in thepth mean. By investigating Lyapunov-like functions and the basic comparison principle, some criteria are derived for various types of practical stability in thepth mean of nonlinear stochastic systems. The main contribution of these results is to convert the problem of practical stability in thepth mean of stochastic systems into the one of practical stability of the comparative deterministic systems.

A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems

1998 ◽  
Vol 65 (4) ◽  
pp. 867-869 ◽  
Author(s):  
J. Q. Sun
Keyword(s):  
Ad Hoc ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Nonlinear Stochastic Systems ◽  
Transition Probability Density ◽  
Generalized Cell Mapping ◽  
One Step ◽  
Step Transition ◽  
The One ◽  
Cell Partition

This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly from being linear to being strongly nonlinear. The nonuniform cell partition is shown to lead to more accurate steady-state solutions and enhance the computational efficiency of the GCM method.

Application of the Adjoint Sensitivity Method to the Analysis of a Supersonic Ejector

1984 ◽  
Vol 106 (4) ◽  
pp. 425-429 ◽  
Author(s):  
E. Wacholder ◽  
J. Dayan
Keyword(s):  
Sensitivity Analysis ◽  
Analysis Method ◽  
Adjoint Sensitivity ◽  
Supersonic Ejector ◽  
Sensitivity Analysis Method ◽  
Manufacturing Tolerances ◽  
Adjoint Functions ◽  
The One ◽  
Sensitivity Method

Although the concepts of various types of ejectors have been thoroughly discussed in the literature during the past sixty years, a rigorous sensitivity analysis of the ejector’s performance has never been presented. In the present work a sensitivity analysis method, based on the use of adjoint functions, is introduced and applied to the one-dimensional model of a supersonic ejector. The advantage of the proposed method over all other possible techniques is that a single computer run can provide the response function sensitivities with respect to all input parameters. The usefulness of the sensitivity coefficients in predicting the ejector’s performance and the uncertainty involved, as well as in the determination of manufacturing tolerances, is demonstrated and proven to be a powerful tool in the design.

A Statistical Study of Generalized Cell Mapping

1988 ◽  
Vol 55 (3) ◽  
pp. 694-701 ◽  
Author(s):  
Jian-Qiao Sun ◽  
C. S. Hsu
Keyword(s):  
Stochastic Systems ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Mapping Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
One Step ◽  
The Mean ◽  
Step Transition ◽  
The One

In this paper a statistical error analysis of the generalized cell mapping method for both deterministic and stochastic dynamical systems is examined, based upon the statistical analogy of the generalized cell mapping method to the density estimation. The convergence of the mean square error of the one step transition probability matrix of generalized cell mapping for deterministic and stochastic systems is studied. For stochastic systems, a well-known trade-off feature of the density estimation exists in the mean square error of the one step transition probability matrix, which leads to an optimal design of generalized cell mapping for stochastic systems. The conclusions of the study are illustrated with some examples.

scholarly journals A limit theorem for Markov chains with continuous state space

1963 ◽  
Vol 3 (3) ◽  
pp. 351-358 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
State Space ◽  
Transition Probabilities ◽  
Borel Subset ◽  
Homogeneous Markov Chain ◽  
Continuous State Space ◽  
Continuous State ◽  
One Step ◽  
Step Transition ◽  
Image Position ◽  
The Right

Let R denote the set of real numbers, B the σ-field of all Borel subsets of R. A homogeneous Markov Chain with state space a Borel subset Ω of R is a sequence {an}, n≧ 0, of random variables, taking values in Ω, with one-step transition probabilities P(1) (ξ, A) defined by for each choice of ξ, ξ0, …, ξn−1 in ω and all Borel subsets A of ω The fact that the right-hand side of (1.1) does not depend on the ξi, 0 ≧ i > n, is of course the Markovian property, the non-dependence on n is the homogeneity of the chain.

A Global Multidimensional Sensitivity Analysis of Electronic Systems Subjected to Time-Dependent Excitations

1998 ◽  
Vol 120 (4) ◽  
pp. 391-394
Author(s):  
H. A. Jensen ◽  
A. O. Cifuentes
Keyword(s):  
Sensitivity Analysis ◽  
Technical Note ◽  
Previous Method ◽  
Design Parameters ◽  
Electronic Systems ◽  
Analysis Method ◽  
Electronic Components ◽  
One Dimensional ◽  
Sensitivity Analysis Method ◽  
The One

This technical note presents a global sensitivity analysis method for the dynamic response of electronic systems considering several design parameters at the same time. The method is an extension of a previous method presented by the authors for the one-dimensional case (only one design variable at a time was considered subjected to uncertainty). The method is expected to be useful in the design, analysis and qualification of electronic components.

A Study on the Rearrangement of Dialkyl 1-Aryl-1-hydroxymethylphosphonates to Benzyl Phosphates

2020 ◽  
Vol 24 (4) ◽  
pp. 465-471 ◽  
Author(s):  
Zita Rádai ◽  
Réka Szabó ◽  
Áron Szigetvári ◽  
Nóra Zsuzsa Kiss ◽  
Zoltán Mucsi ◽  
...  
Keyword(s):  
Quantum Chemical ◽  
Room Temperature ◽  
Phase Transfer ◽  
One Pot ◽  
Substrate Dependence ◽  
Triethylbenzylammonium Chloride ◽  
One Step ◽  
The Pudovik Reaction ◽  
The One ◽  
Solid Liquid

The phospha-Brook rearrangement of dialkyl 1-aryl-1-hydroxymethylphosphonates (HPs) to the corresponding benzyl phosphates (BPs) has been elaborated under solid-liquid phase transfer catalytic conditions. The best procedure involved the use of triethylbenzylammonium chloride as the catalyst and Cs2CO3 as the base in acetonitrile as the solvent at room temperature. The substrate dependence of the rearrangement has been studied, and the mechanism of the transformation under discussion was explored by quantum chemical calculations. The key intermediate is an oxaphosphirane. The one-pot version starting with the Pudovik reaction has also been developed. The conditions of this tandem transformation were the same, as those for the one-step HP→BP conversion.

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