Competing particle systems evolving by interacting Lévy processes

DOI10.1214/10-AAP743zbMath1238.60113arXiv1002.2811MaRDI QIDQ655586

Mykhaylo Shkolnikov

Publication date: 4 January 2012

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.2811

zbMATH Keywords

Lévy processesstochastic differential equationsHarris recurrencecapital distributionsLévy queueing networkssemimartingale reflected Brownian motions

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Auctions, bargaining, bidding and selling, and other market models (91B26)

Related Items (21)

Diverse market models of competing Brownian particles with splits and mergers ⋮ Optimal surviving strategy for drifted Brownian motions with absorption ⋮ Two-Sided Infinite Systems of Competing Brownian Particles ⋮ Concentration for multidimensional diffusions and their boundary local times ⋮ Large systems of diffusions interacting through their ranks ⋮ Infinite systems of competing Brownian particles ⋮ Long time behaviour and mean-field limit of Atlas models ⋮ Backward stochastic differential equations with rank-based data ⋮ Convergence rates for rank-based models with applications to portfolio theory ⋮ Strong solutions of stochastic equations with rank-based coefficients ⋮ On a class of diverse market models ⋮ Modeling flocks and prices: jumping particles with an attractive interaction ⋮ Comparison techniques for competing Brownian particles ⋮ A stock market model based on CAPM and market size ⋮ Stationary distributions of the Atlas model ⋮ Exponential ergodicity and convergence for generalized reflected Brownian motion ⋮ A note on jump Atlas models ⋮ Concentration of measure for Brownian particle systems interacting through their ranks ⋮ Reflected backward stochastic differential equation with rank-based data ⋮ The infinite Atlas process: convergence to equilibrium ⋮ Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-Line

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