Reaction-diffusion models for a class of infinite-dimensional nonlinear stochastic differential equations. (English) Zbl 1516.60043
The authors establish the existence of solutions to a class of nonlinear stochastic differential equations in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. These equations can be used to model a reaction-diffusion system associated for instance with chemical reactions or population dynamics.
Reviewer: Alexandra Rodkina (College Station)
MSC:
| 60J25 | Continuous-time Markov processes on general state spaces |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 35K57 | Reaction-diffusion equations |
Keywords:
reaction-diffusion models; scaling limits of particle systems; martingale problems; thermodynamic limitReferences:
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