IA Scholar Query: Simulation Hemi-metrics between Infinite-State Stochastic Games.
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Internet Archive Scholar query results feedeninfo@archive.orgSun, 24 Apr 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A Generic Approach to Quantitative Verification
https://scholar.archive.org/work/s4ktcdwunvgwtitzak6shoutim
This thesis is concerned with quantitative verification, that is, the verification of quantitative properties of quantitative systems. These systems are found in numerous applications, and their quantitative verification is important, but also rather challenging. In particular, given that most systems found in applications are rather big, compositionality and incrementality of verification methods are essential. In order to ensure robustness of verification, we replace the Boolean yes-no answers of standard verification with distances. Depending on the application context, many different types of distances are being employed in quantitative verification. Consequently, there is a need for a general theory of system distances which abstracts away from the concrete distances and develops quantitative verification at a level independent of the distance. It is our view that in a theory of quantitative verification, the quantitative aspects should be treated just as much as input to a verification problem as the qualitative aspects are. In this work we develop such a general theory of quantitative verification. We assume as input a distance between traces, or executions, and then employ the theory of games with quantitative objectives to define distances between quantitative systems. Different versions of the quantitative bisimulation game give rise to different types of distances, viz.~bisimulation distance, simulation distance, trace equivalence distance, etc., enabling us to construct a quantitative generalization of van Glabbeek's linear-time--branching-time spectrum. We also extend our general theory of quantitative verification to a theory of quantitative specifications. For this we use modal transition systems, and we develop the quantitative properties of the usual operators for behavioral specification theories.Uli Fahrenbergwork_s4ktcdwunvgwtitzak6shoutimSun, 24 Apr 2022 00:00:00 GMTCentral Limit Theory for Models of Strategic Network Formation
https://scholar.archive.org/work/z4wsi5jtinfkzpasce2qdy55cm
We provide asymptotic approximations to the distribution of statistics that are obtained from network data for limiting sequences that let the number of nodes (agents) in the network grow large. Network formation is permitted to be strategic in that agents' incentives for link formation may depend on the ego and alter's positions in that endogenous network. Our framework does not limit the strength of these interaction effects, but assumes that the network is sparse. We show that the model can be approximated by a sampling experiment in which subnetworks are generated independently from a common equilibrium distribution, and any dependence across subnetworks is captured by state variables at the level of the entire network. Under many-player asymptotics, the leading term of the approximation error to the limiting model established in Menzel (2015b) is shown to be Gaussian, with an asymptotic bias and variance that can be estimated consistently from a single network.Konrad Menzelwork_z4wsi5jtinfkzpasce2qdy55cmTue, 02 Nov 2021 00:00:00 GMTLarge Deviations of Irreversible Processes
https://scholar.archive.org/work/oenrwsc7mzh3hlwibznzmirkmi
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large deviation theory. We focus on processes that become deterministic in a certain limit, and characterize their fluctuations around that deterministic limit by Lagrangian rate functions. Our main techniques for establishing these characterizations rely on the connection between large deviations and Hamilton-Jacobi equations. We sketch this connection with examples in the introductory parts of this thesis. The second part of the thesis is devoted to irreversible processes that are motivated from molecular motors, Markov chain Monte Carlo (MCMC) methods and stochastic slow-fast systems. We characterize the asymptotic dynamics of molecular motors by Hamiltonians defined in terms of principal-eigenvalue problems. From our results about the zig-zag sampler used in MCMCs, we learn that maximal irreversibility corresponds to an optimal rate of convergence. In stochastic slow-fast systems, our main theoretical contributions are techniques to work with the variational formulas of Hamiltonians that one encounters in mean-field systems coupled to fast diffusions. In the final part of the thesis, we study a family of Fokker-Planck equations whose solutions become singular in a certain limit. The associated gradient-flow structures do not converge since the relative entropies diverge in the limit. To remedy this, we propose to work with a different variational formulation that takes fluxes into account, which is motivated by density-flux large deviations.Mikola C. Schlottkework_oenrwsc7mzh3hlwibznzmirkmiSun, 19 Sep 2021 00:00:00 GMT