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3 questions
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Stochastic stability of "open" continuous-time stochastic systems: reference request
I'm looking for results on the stability of stochastic systems, e.g. SDEs, whose coefficients depend on a different process that is not necessarily stable. I'm calling those systems "open" here, but ...
- 1,675
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If a probability measure is stationary in both forward time and reverse time, does this imply that the measure is incompressible?
Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and let $X$ be a compact metric space. Let $F \colon \Omega \times X \to X$ and $\bar{F} \colon \Omega \times X \to X$ be measurable ...
- 708
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In smooth stochastic dynamics, if a Lebesgue-like measure is both forward-time and reverse-time stationary, is the measure necessarily incompressible?
Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and let $X$ be a compact connected $C^\infty$-smooth manifold. Let $F \colon \Omega \times X \to X$ and $\bar{F} \colon \Omega \times X \to ...
- 708