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The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift [article]

Raphael Kruse, Rico Weiske
2021 arXiv   pre-print
We study the numerical approximation of stochastic evolution equations with a monotone drift driven by an infinite-dimensional Wiener process.  ...  To discretize the equation, we combine a drift-implicit two-step BDF method for the temporal discretization with an abstract Galerkin method for the spatial discretization.  ...  Acknowledgment The authors like to thank Etienne Emmrich for very helpful comments on the BDF2 method for nonlinear evolution equations.  ... 
arXiv:2105.08767v1 fatcat:lfxepcoasrbztomnsquxnc5bxa

Generalized Monotonicity Analysis

Bruno H. Strulovici, Thomas A. Weber
2006 Social Science Research Network  
Second, it allows studying the monotonicity of functions or subsets of variables. Third, GMA naturally provides bounds on the sensitivity of variables to parameter changes.  ...  Generalized monotonicity analysis (GMA) extends the available methods in several directions. First, it provides a way of finding parameter moves that yield monotonicity of model solutions.  ...  For a fixed t k+1 , the solution x(t) is nondecreasing in s k and thus depends only on s k , by induction hypothesis. Thus, x depends only on s k and t k+1 .  ... 
doi:10.2139/ssrn.951732 fatcat:siebhjf7mjag3phhgg2h4gig6i

Generalized monotonicity analysis

Bruno H. Strulovici, Thomas A. Weber
2009 Economic Theory  
Second, it allows studying the monotonicity of functions or subsets of variables. Third, GMA naturally provides bounds on the sensitivity of variables to parameter changes.  ...  Generalized monotonicity analysis (GMA) extends the available methods in several directions. First, it provides a way of finding parameter moves that yield monotonicity of model solutions.  ...  For a fixed t k+1 , the solution x(t) is nondecreasing in s k and thus depends only on s k , by induction hypothesis. Thus, x depends only on s k and t k+1 .  ... 
doi:10.1007/s00199-009-0450-4 fatcat:hhelgwyyunaknjydl7p5hgx7ly

Monotone imitation

Carlos Oyarzun, Johannes Ruf
2008 Economic Theory  
We say that a behavioral rule is first-order monotone (FOM) if the number of individuals who play actions with first-order stochastic dominant payoff distributions is expected to increase in any environment  ...  In economics, an important role for learning and evolution theory is providing an analytical framework to asses when experience will lead individuals to behave as rational agents (for example, see the  ...  In order to allow for experimentation, in this section we allow behavioral rules to depend on time.  ... 
doi:10.1007/s00199-008-0398-9 fatcat:iurk53ulpjaebdn6nfoaxphh6u

On monotone convolution and monotone infinite divisivility [article]

Takahiro Hasebe
2010 arXiv   pre-print
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied.  ...  Nobuaki Obata for giving him an opportunity to present this research in Tohoku University. He is also grateful to Prof. Shogo Tanimura, Mr. Hayato Saigo, Mr. Ryo Harada, Mr. Hiroshi Ando, Mr.  ...  Acknowledgments The author expresses his great appreciation to Prof. Izumi Ojima for his warm encouragements and valuable suggestions during his master course. He thanks Prof.  ... 
arXiv:1002.3430v2 fatcat:bxvmcygmlzbtviwepev42uq6cq

Generating monotone quantities for the heat equation [article]

Jonathan Bennett, Neal Bez
2017 arXiv   pre-print
The purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations in euclidean  ...  This framework is intimately connected to the existence of a rich variety of algebraic closure properties of families of sub/super-solutions, and more generally solutions of systems of differential inequalities  ...  Introduction The identification of functionals which vary monotonically as their inputs flow according to a given evolution equation is generally considered to be more of an art than a science.  ... 
arXiv:1509.01949v2 fatcat:ijqwp24p6rcuhn5day65w4xj7q

Monotone Learning with Rectified Wire Networks [article]

Veit Elser, Dan Schmidt, Jonathan Yedidia
2019 arXiv   pre-print
We introduce a new neural network model, together with a tractable and monotone online learning algorithm.  ...  Our model describes feed-forward networks for classification, with one output node for each class. The only nonlinear operation is rectification using a ReLU function with a bias.  ...  We also thank the three reviewers whose comments brought significant improvements to the paper.  ... 
arXiv:1805.03963v4 fatcat:aracjw74yjcelnp6jy5ot2j2di

Generating monotone quantities for the heat equation

Jonathan Bennett, Neal Bez
2017 Journal für die Reine und Angewandte Mathematik  
AbstractThe purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations  ...  This framework is intimately connected to the existence of a rich variety of algebraic closure properties of families of sub/super-solutions, and more generally solutions of systems of differential inequalities  ...  Introduction The identification of functionals which vary monotonically as their inputs flow according to a given evolution equation is generally considered to be more of an art than a science.  ... 
doi:10.1515/crelle-2017-0025 fatcat:cpvsypbd3fagte56hafexdfcyy

Expedient and Monotone Learning Rules

Tilman Borgers, Antonio J. Morales, Rajiv Sarin
2004 Econometrica  
This paper considers learning rules for environments in which little prior and feedback information is available to the decision maker.  ...  Two properties of such learning rules are studied: absolute expediency and monotonicity.  ...  Our analysis could form a building block for an analysis that includes a study of the optimal initial point for the learning process.  ... 
doi:10.1111/j.1468-0262.2004.00495.x fatcat:3pm5i3wcsjb6nh7ame2zzzzyji

Formal Synthesis of Control Strategies for Positive Monotone Systems

Sadra Sadraddini, Calin Belta
2018 IEEE Transactions on Automatic Control  
We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances.  ...  We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions.  ...  We use monotonicity to provide an alternative approach. Definition 7.  ... 
doi:10.1109/tac.2018.2814631 fatcat:7dqyiozo4nhmhjh3ouz5uylywy

Localization for alloy-type models with non-monotone potentials [article]

Martin Tautenhahn
2012 arXiv   pre-print
This Wegner estimate is applicable for a proof of localization via multiscale analysis.  ...  This thesis refines the methods of multiscale analysis and fractional moments in the case where the single-site potential is allowed to change its sign.  ...  It follows from our definition, that the randomness of H Γ at sites ∂ oŴ x ∩Γ does not depend on the random variables ω b for any b ∈ B x , and depends monotonically on the random variables ω k for k ∈  ... 
arXiv:1211.3891v1 fatcat:bkj5moseq5b2jkk7mii3pbfeke

Monotone dynamical systems [chapter]

Hal Smith
2008 Mathematical Surveys and Monographs  
The dynamics of cone-preserving operators continues to play an important role in functional analysis; for a survey, see Nussbaum [145, 146] .  ...  An alternative is to establish the monotonicity properties on the larger spaces first and then get corresponding properties on the smaller spaces by restriction.  ... 
doi:10.1090/surv/041/01 fatcat:claelccfvnbajbkse2ajycf6ci

Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation [article]

Sidhant Misra, Marc Vuffray, Anatoly Zlotnik
2020 arXiv   pre-print
of monotone ordering of states with respect to time-varying boundary condition parameters.  ...  For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation  ...  Then the evolution of nodal density variables for the system, according to Eq. (29), satisfies ρ i (t) for all t ∈ [0, T ] and for all i ∈ V.  ... 
arXiv:2007.10271v1 fatcat:ku5ityt67jcxndwgohryos7kme

Automatic Parallelization Using the Value Evolution Graph [chapter]

Silvius Rus, Dongmin Zhang, Lawrence Rauchwerger
2005 Lecture Notes in Computer Science  
We introduce a framework for the analysis of memory reference sets addressed by induction variables without closed forms.  ...  We describe the application of our framework to array dataflow analysis, privatization, and dependence analysis.  ...  We are also looking into further applications of value evolution graphs to the GSA path technique.  ... 
doi:10.1007/11532378_27 fatcat:3ay57pbe3rc5hj2vzoizmf4n7e

Convergence analysis of some multivariate Markov chains using stochastic monotonicity

Kshitij Khare, Nabanita Mukherjee
2013 The Annals of Applied Probability  
It is shown that all these Markov chains are stochastically monotone with respect to an appropriate partial ordering.  ...  We provide a nonasymptotic analysis of convergence to stationarity for a collection of Markov chains on multivariate state spaces, from arbitrary starting points, thereby generalizing results in [Khare  ...  random variables X and Y such that X ∼ µ, Y ∼ ν and X Y; see for example [8] .  ... 
doi:10.1214/12-aap856 fatcat:kicih5cj5rc3nch6vdsa3lfvfa
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