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Stationarity of Stochastic Linear Equations with additive noise and delays in the unbounded drift terms.
Liu Kai (刘凯) 教授(英国Liverpool大学数学系)
2018-01-01 12:13  华东师范大学

摘要: This talk is about the stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated stochastic equations have unbounded operators acting on the discrete or distributed delayed terms, while the operator acting on the instantaneous term generates a strongly continuous semigroup. We present conditions on the delay systems to obtain a unique stationary solution by combining spectrum analysis of unbounded operators and stochastic calculus. A few instructive cases are analyzed in detail to clarify the underlying complexity in the study of systems with unbounded delayed operators..