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arXiv · 1408.0933

Blow-up of a stable stochastic differential equation

Matti Leimbach·Michael Scheutzow
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Abstract

We examine a 2-dimensional ODE which exhibits explosion in finite time. Considered as an SDE with additive white noise, it is known to be complete - in the sense that for each initial condition there is almost surely no explosion. Furthermore, the associated Markov process even admits an invariant probability measure. On the other hand, as we will show, the corresponding local stochastic flow will almost surely not be strongly complete, i.e.~there exist (random) initial conditions for which the solutions explode in finite time.

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Matti Leimbach, Michael Scheutzow. 2014-08-05. Blow-up of a stable stochastic differential equation. https://arxiv.org/abs/1408.0933

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