I've been reading Oksendal, and it's quite tedious. It want to see if my understanding of the motivation and process is correct.(adsbygoogle = window.adsbygoogle || []).push({});

1) Differential equations that have random variables need special techniques to be solved

2) Ito and Stratonovich extended calculus to apply to random variables.

3) Oksendal uses Ito/Stratonovch calculus to solve differential equations.

4) This method works by converting the differential equation into a recurrence relations (e.g. of the form x(t+1) = x(t)+dt*(a*x(t)+'noise'))

5) This sort of problem can be solved. I.e. The probability P(x(t+1)) can be solved by convolving P(x(t)) with the probability of everything in dt term.

What other nuggets of info should I be taking away from this book?

Are there other techniques for solving stochastic differential equations that don't require converting into recurrence relations?

For EE people, they're typically happy once they have the filter frequency response.

It would be cool to see an over view of how each field (bio, physics, finance, EE, etc...) deals with randomness.

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# Stochastic differential equations question. An over view

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