Solutions of a class of nonlinear master equations

DOI10.1016/0304-4149(92)90076-3zbMath0762.60075OpenAlexW2036104705MaRDI QIDQ1201759

S. Singh

Publication date: 17 January 1993

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(92)90076-3

zbMATH Keywords

phase transitionmaster equationmartingale problemstationary distributionsSkorokhod space\(Q\)-matrixbirth- death modelsecond Schlögl model

Mathematics Subject Classification ID

Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (15)

On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators ⋮ Large deviations for Markov processes with mean field interaction and unbounded jumps ⋮ Nonlinear master equation of multitype particle systems ⋮ Critical phenomenon of a two component nonlinear stochastic system ⋮ Mean-field risk sensitive control and zero-sum games for Markov chains ⋮ Derivation of mean-field equations for stochastic particle systems ⋮ Uniqueness of stationary distribution and exponential convergence for distribution dependent SDEs ⋮ Existence and non-uniqueness of stationary distributions for distribution dependent SDEs ⋮ A stochastic maximum principle for Markov chains of mean-field type ⋮ Law of large numbers and central limit theorem for unbounded jump mean- field models ⋮ Reaction-diffusion processes ⋮ Optimal control and zero-sum games for Markov chains of mean-field type ⋮ Balancing queues by mean field interaction ⋮ Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications ⋮ Phase transitions for a class of time-inhomogeneous diffusion processes

Cites Work

• The diffusion approximation of the spatially homogeneous Boltzmann equation
• A martingale approach to infinite systems of interacting processes
• A certain class of diffusion processes associated with nonlinear parabolic equations
• Central limit theorem for a system of Markovian particles with mean field interactions
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