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Stability, Stationarity, Ergodicity

  • Vincenzo Capasso
  • David Bakstein
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

Here we shall consider multidimensional diffusion processes {u(t), t ∈ I} in \(\mathbb{R}^{d},\) (\(d \in \mathbb{N}\setminus \{0\}\)) solution on a time interval \(I \subset \mathbb{R}_{+}\) of a d−dimensional system of stochastic differential equations of the form
$$\displaystyle{ d\mathbf{u}(t) = \mathbf{a}(t,\mathbf{u}(t))dt + b(t,\mathbf{u}(t))d\mathbf{W}(t), }$$
(5.1)
subject to a suitable initial condition.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vincenzo Capasso
    • 1
  • David Bakstein
    • 1
  1. 1.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)Università degli Studi di MilanoMilanItaly

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