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Analytic and locally approximate solutions to properties of probabilistic processes [chapter]

C. Tofts
1995 Lecture Notes in Computer Science  
We present how analytic formulae for performance properties can be derived from probabilistic process algebraic descriptions; demonstrating how local approximate solutions can be derived for the properties  ...  Recent extensions to process algebra can be used to describe performance or error rate properties of systems. We examine how properties of systems expressed in these algebras can be elicited.  ...  The generation of local approximations to the solutions of systems is of great importance.  ... 
doi:10.1007/3-540-60630-0_9 fatcat:6pmtyodv3nbqjjcntlxzezfnl4

A probabilistic model for the numerical solution of initial value problems [article]

Michael Schober, Simo Särkkä, Philipp Hennig
2017 arXiv   pre-print
This probabilistic formulation of classic methods is valuable in two ways: analytically, it highlights implicit prior assumptions favoring certain approximate solutions to the IVP over others, and gives  ...  We describe a class of algorithms that formulate the solution to an IVP as inference on a latent path that is a draw from a Gaussian process probability measure (or equivalently, the solution of a linear  ...  The authors also thank the feedback of the anonymous reviewers which helped to improve the presentation significantly.  ... 
arXiv:1610.05261v3 fatcat:vxip7z3nxfbuhdwlgan6h2ihri

Bayesian Filtering for ODEs with Bounded Derivatives [article]

Emilia Magnani, Hans Kersting, Michael Schober, Philipp Hennig
2017 arXiv   pre-print
process (IWP) filter by encoding the property that a derivative in time of the solution is bounded in the sense that it tends to drift back to zero.  ...  Recently there has been increasing interest in probabilistic solvers for ordinary differential equations (ODEs) that return full probability measures, instead of point estimates, over the solution and  ...  ' to the mean, whereas the IOUP solver remains closer to the solution due to the process drifting property and smaller variance.  ... 
arXiv:1709.08471v1 fatcat:xmi3eaglqvcwnn4u7wkjgmtqyu

A probabilistic model for the numerical solution of initial value problems

Michael Schober, Simo Särkkä, Philipp Hennig
2018 Statistics and computing  
We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate  ...  Adding to this picture, we show that several multistep methods of Nordsieck form can be recasted as Kalman filtering on q-times integrated Wiener processes.  ...  In this paper, we present a class of probabilistic solvers which combine properties of the standard and the probabilistic algorithms.  ... 
doi:10.1007/s11222-017-9798-7 fatcat:tzqmajvuobb2lfss7cwpjk4xlu

Optimization of static traffic allocation policies

M.B. Combé, O.J. Boxma
1994 Theoretical Computer Science  
Two static policies are considered: probabilistic assignment and allocation according to a fixed pattern. For these two policies, general properties as well as optimization aspects are discussed.  ...  We consider the traffic allocation problem: arriving customers have to be assigned to one of a group of servers.  ...  Due to this property, there is only one local minimum, which consequently has to be the optimal solution for the allocation problem.  ... 
doi:10.1016/0304-3975(94)90292-5 fatcat:tmjokcy4yjhb3pzutgk36yr6su

Optimal, Robust Predictive Control of Nonlinear Systems under Probabilistic Uncertainty using Particles

Lars Blackmore, Brian C. Williams
2007 American Control Conference (ACC)  
Any solution returned by the algorithm is guaranteed to be -close to a local optimum of the nonlinear stochastic control problem.  ...  In this paper we present a novel method for robust, optimal control of nonlinear systems under probabilistic uncertainty.  ...  By solving this deterministic problem we obtain an approximate solution to the original stochastic problem, with the additional property that as the number of particles used tends to infinity, the approximation  ... 
doi:10.1109/acc.2007.4282699 dblp:conf/acc/BlackmoreW07 fatcat:vupvswykrrfolfzxaz6cjmgv6e

Optimization of static traffic allocation policies

M Combé
1994 Theoretical Computer Science  
Two static policies are considered: probabilistic assignment and allocation according to a fixed pattern. For these two policies, general properties as well as optimization aspects are discussed.  ...  We consider the traffic allocation problem: arriving customers have to be assigned to one of a group of servers.  ...  Borst for valuable suggestions concerning the algorithm for constructing an allocation pattern, and to G.M. Koole for interesting discussions.  ... 
doi:10.1016/0304-3975(94)90215-1 fatcat:4akdz3x6irf2nesgjcvkdfu7oi

Stochastic Finite-Element Analysis of Seismic Soil–Structure Interaction

Dan M. Ghiocel, Roger G. Ghanem
2002 Journal of engineering mechanics  
The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented  ...  Uncertain parameters are modeled using a probabilistic framework as stochastic processes.  ...  Acknowledgments The financial support of the National Science Foundation through the SBIR and Geomechanics programs under Grant Nos.  ... 
doi:10.1061/(asce)0733-9399(2002)128:1(66) fatcat:eqsfqgzsnjaoddnbx27w6ohyxq

CONTENTS [chapter]

1992 Analytic and Probabilistic Methods in Number Theory  
On the Arithmetic Properties of the Values of ^-Functions On Some Formulae in Analytic Number Theory. IIVII.  ...  COMPUTATIONAL NUMBER THEORY AND APPLICATIONS TO NUMERIC ANALYSISOn Normal Bases of Algebraic Number Fields S. A. Stepanov and I. E. Shparlinski 369 Number Theory and Number Crunching P.  ... 
doi:10.1515/9783112314234-toc fatcat:u763j4kymffwbp3bc74rz2x77q

Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion equations

Eric M. LaBolle, Jeremy Quastel, Graham E. Fogg
1998 Water Resources Research  
Derivation of ADEs from probabilistic assumptions yields (1) necessary conditions for convergence of diffusion processes to ADEs, even when coefficients are discontinuous, and (2) general probabilistic  ...  Local-scale spatial averaging of pore-scale advection-diffusion equations in porous media leads to advection-dispersion equations (ADEs).  ...  Success with the method of Uffink [1985] confirms the ob-vious: transition-probability densities of Markov-chain approximations to ADEs may be constructed from an analytical solution to the governing  ... 
doi:10.1029/98wr00319 fatcat:ajcagfegoregthocqiyw63pvgm

Page 4212 of Mathematical Reviews Vol. , Issue 84j [page]

1984 Mathematical Reviews  
They study convergence to Poisson and Wiener processes, processes with independent increments, and to solutions of stochastic equations.  ...  The basic idea of the proofs consists in the construction of an approximating sequence of equations having strong solutions, with subsequent reconstruction of weak compactness of a sequence of these solutions  ... 

Page 8026 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
) On probabilistic properties of nonlinear AR MA(p, q) models.  ...  The authors prove existence and uniqueness of the solution. They also get estimates on the convergence rate of empirical measures of particle systems to the solution of the balance equation.  ... 

Approximate and Probabilistic Computing: Design, Coding, Verification (Dagstuhl Seminar 15491)

Antonio Filieri, Marta Kwiatkowska, Sasa Misailovic, Todd Mytkowicz, Marc Herbstritt
2016 Dagstuhl Reports  
The aim of this seminar was to bring together academic and industrial researchers from the areas of probabilistic model checking, quantitative software analysis, probabilistic programming, and approximate  ...  Millions of people already use software which computes with and reasons about approximate/probabilistic data daily.  ...  For instance, multimedia processing, machine learning, and big-data analytics applications perform approximate operations on large data sets.  ... 
doi:10.4230/dagrep.5.11.151 dblp:journals/dagstuhl-reports/FilieriKMM15 fatcat:dao63covdjhflma6fflt3meus4

Probability Measures for Numerical Solutions of Differential Equations [article]

Patrick R. Conrad, Mark Girolami, Simo Särkkä, Andrew Stuart, Konstantinos Zygalakis
2015 arXiv   pre-print
Numerical solutions of differential equations contain inherent uncertainties due to the finite dimensional approximation of an unknown and implicitly defined function.  ...  In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models.  ...  While we argue that the choice of modelling local uncertainty in the flow-map as a Gaussian process is natural and analytically favourable, it is not unique.  ... 
arXiv:1506.04592v1 fatcat:fqv5xyeirjdz3gop5avhxepdta

Tight Probabilistic SINR Constrained Beamforming Under Channel Uncertainties

Xin He, Yik-Chung Wu
2015 IEEE Transactions on Signal Processing  
Therefore, existing probabilistic beamforming methods focus on the relatively simple Gaussian and uniform channel uncertainties, and mainly rely on probability inequality based approximated solutions,  ...  In this paper, based on the local structure of the feasible set in the probabilistic beamforming problem, a systematic method is proposed to realize tight SINR outage control for a large class of channel  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their constructive comments that helped to improve the paper.  ... 
doi:10.1109/tsp.2015.2425806 fatcat:hx7leml7dvemnpmy3p3zgil3hi
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