Qualitative Theory of Stochastic Non-Linear Systems

  • Ludwig Arnold
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 8)


The aim of this survey paper is to sketch the problems and results of the qualitative theory of stochastic dynamical systems (SDS) and to give reference to papers where details can be found. Here an SDS is an ordinary differential equation ẋ = f (x,ξ) with a random noise process ξ in the r.h.s. and random initial conditions x(o) = xo. Qualitative theory studies the general nature of a solution in the entire time interval, e.g. recurrence and stability properties. Both the white noise and the real (i.e. non-white) noise case are covered. Emphasis is given to nonlinear systems (including multiplicative noise linear systems) and to stationary and Markovian noise. Standing reference is ARNOLD and KLIEMANN [7].


Multiplicative Noise Qualitative Theory Stochastic Nonlinear System Random Initial Condition Stochastic Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Ludwig Arnold
    • 1
  1. 1.Fachbereich MathematikUniversität BremenBremenFed. Rep. of Germany

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