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# Random process

edited January 2015

Created page Random Process.

There are two aspects I have in mind: First, provide background material for the statistical analysis of time series, which is a central part of all Earth sciences.

Second, link to implementation issues of models including random elements, like stochastic climate models.

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1.

Wow - "random process" gets us into very broad scientific issues!

But we can see how the page grows and rename it later if desired.

Comment Source:Wow - "random process" gets us into very broad scientific issues! But we can see how the page grows and rename it later if desired.
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2.
edited October 2010

I certainly don't intend to construct Brownian motion by invoking Kolomogorov's extension theorem on this page...but I do need to write a little bit about random number generators, because Wikipedia and other web resources are outdated in this regard, and I don't like isolated pages, so I needed one to link climate modelling with random number generation...

Comment Source:I certainly don't intend to construct Brownian motion by invoking Kolomogorov's extension theorem on this page...but I do need to write a little bit about random number generators, because Wikipedia and other web resources are outdated in this regard, and I don't like isolated pages, so I needed one to link climate modelling with random number generation...
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3.

I couldn't resist the urge to hint at Kolmogorov extension, before I saw this thread...

Anyway, I made the text a little longer - mostly the idea that one can view the stochastic differential equations as consistency conditions on a bunch of random observables which may live at different times. Mathematically, I think it's much cleaner to consider SDEs as a sort of shorthand for stochastic integral equations, which are easier to define rigorously than what one means by dW.

I don't want to go into functional analysis on the wiki, but I may bring in some qualitative ideas in that vein.

All hail the Gelfand-Naimark construction! :-P

Comment Source:I couldn't resist the urge to hint at Kolmogorov extension, before I saw this thread... Anyway, I made the text a little longer - mostly the idea that one can view the stochastic differential equations as consistency conditions on a bunch of random observables which may live at different times. Mathematically, I think it's much cleaner to consider SDEs as a sort of shorthand for stochastic integral equations, which are easier to define rigorously than what one means by dW. I don't want to go into functional analysis on the wiki, but I may bring in some qualitative ideas in that vein. All hail the Gelfand-Naimark construction! :-P
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4.

Added the start of a section called "Mathematical definition."

I'm planning to flesh this out a bit, and add some examples.

Comment Source:Added the start of a section called "Mathematical definition." I'm planning to flesh this out a bit, and add some examples.