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Stochastic Resonance in Infinite Dimensions

+ 4 like - 0 dislike
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I'll ask this from the point of view of physics more than of theoretical mathematics. I'm searching for a mathematical discussion of stochastic resonance interpreted in a PDE sense. This is a good mathematical discussion of the one dimensional case: http://www.univ-orleans.fr/mapmo/membres/berglund/noisres.html. I'll gladly discuss what I think is important about this from the point of view of theoretical physics, but in the comments. I'm not even sure if a discussion about the SPDE case corresponding to that even exists, so it may well be worth it to open up one in this medium.

Here's an example of what might interest a physics audience: what's the relationship between stochastic resonance and the Boltzmann equation?

I would also love to be linked to protocols for doing "experiments" in SPDE, for example powerful simulations of noise.

(To be one hundred percent clear, the trajectory of the particle shown in the videos in that website's exposition should be extended here to a trajectory in an infinite dimensional Banach space)

This post imported from StackExchange MathOverflow at 2015-02-15 12:16 (UTC), posted by SE-user Ravi Andrew Bajaj
asked Jan 10, 2015 in Theoretical Physics by Ravi Andrew Bajaj (20 points) [ no revision ]
retagged Feb 15, 2015
One place to start for the interest in stochastic resonance that's been, at least for me, local here in Cambridge is a video on the progress of Jeremy England, which was posted by the MIT Physics Department. Here it is: <youtube.com/watch?v=ka8573QQKW4&feature=youtu.be&gt;

This post imported from StackExchange MathOverflow at 2015-02-15 12:16 (UTC), posted by SE-user Ravi Andrew Bajaj
Consider G. da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions (1992). If I remember correctly they also discuss asymptotic properties of solutions, besides the usual existence, uniqueness and continuous dependence properties.

This post imported from StackExchange MathOverflow at 2015-02-15 12:16 (UTC), posted by SE-user Uwe Stroinski

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