How can Fubini's Theorem be applied to solve more complex integrals?

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In summary, the conversation discusses a specific integration problem and the use of Fubini's theorem to solve it. The speaker is struggling to understand the application of Fubini's theorem and is seeking more information and examples. They mention that they already know the answer and are interested in using Fubini's theorem rather than integration by parts. A resource is provided for further help with the application of Fubini's theorem.
  • #1
johnny.wi
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I am really stuck on this and can't find any information or examples on it. My textbook has one example in it and it isn't explained at all. It is the following?

∫B{s}ds

integrated From 0 to t.It is then changed to a double integral and fubinis theorm is applied to arrive at the solution by changing the limits of integration and odrer of integration, with no explanation as to the method.


This is easy to solve with integration by parts, but i am trying to figure out how to use fubinis theorm and how to change the limits of integration so i can apply the method to some more elaborate integrals.
I already now the anser and that it is normally distributed, i am inerested in the application of fubinis theorm and not integration by parts.
 
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  • #2
johnny.wi said:
I am really stuck on this and can't find any information or examples on it. My textbook has one example in it and it isn't explained at all. It is the following?

∫B{s}ds

integrated From 0 to t.It is then changed to a double integral and fubinis theorm is applied to arrive at the solution by changing the limits of integration and odrer of integration, with no explanation as to the method.


This is easy to solve with integration by parts, but i am trying to figure out how to use fubinis theorm and how to change the limits of integration so i can apply the method to some more elaborate integrals.
I already now the anser and that it is normally distributed, i am inerested in the application of fubinis theorm and not integration by parts.

Perhaps this might help:

http://math.stackexchange.com/questions/83239/application-of-fubinis-theorem
 

Related to How can Fubini's Theorem be applied to solve more complex integrals?

What is the Stochastic Fubini Theorem?

The Stochastic Fubini Theorem is a mathematical concept that states the order of integration can be exchanged in certain double integrals involving stochastic processes. It is used in probability theory and stochastic calculus.

What are the applications of the Stochastic Fubini Theorem?

The Stochastic Fubini Theorem is used in various fields such as finance, economics, and physics. It is commonly used in the study of stochastic processes, which are random processes that evolve over time. It is also used in the pricing and hedging of financial derivatives.

What is the difference between the Stochastic Fubini Theorem and the regular Fubini Theorem?

The regular Fubini Theorem is a mathematical concept that states the order of integration can be exchanged in certain double integrals involving real-valued functions. The Stochastic Fubini Theorem is an extension of this concept to integrals involving stochastic processes. In other words, the Stochastic Fubini Theorem deals with integrals involving random variables and the regular Fubini Theorem deals with integrals involving deterministic functions.

Can the Stochastic Fubini Theorem be generalized to higher dimensions?

Yes, the Stochastic Fubini Theorem can be extended to integrals involving more than two variables and can be applied to higher dimensions. This is known as the Stochastic Fubini Theorem for multiple integrals and has various applications in the study of multi-dimensional stochastic processes.

What are the assumptions for the Stochastic Fubini Theorem to hold?

The Stochastic Fubini Theorem holds under certain conditions such as the integrals being absolutely convergent, the stochastic processes being independent, and the functions being measurable. Additionally, the theorem holds when the integrand is an adapted stochastic process and the integrals are taken over a bounded region.

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