Integrating Factors for Stochastic Differential Equations

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Homework Help Overview

The discussion revolves around the concept of integrating factors in stochastic differential equations (SDEs). The original poster expresses a desire to understand how to derive these integrating factors, which are typically provided as hints in problems. Examples of SDEs and their corresponding integrating factors are mentioned.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to seek a method for deriving integrating factors for various SDEs, questioning the reliance on provided hints. Some participants suggest that integrating factors will be covered in future coursework, while others note the relevance of ordinary differential equations to the topic.

Discussion Status

The discussion is ongoing, with participants sharing perspectives on the learning process and the applicability of integrating factors. There is a recognition of differing educational backgrounds, with some participants providing material related to ordinary differential equations, although its direct relevance to SDEs is questioned.

Contextual Notes

There is mention of the original poster's current coursework in financial mathematics and stochastic calculus, indicating a potential gap in the curriculum regarding the derivation of integrating factors. The discussion also highlights the distinction between ordinary and stochastic differential equations.

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Whenever I'm given a SDE problem that requires us to multiply both sides by an "integrating-factor", it's always given to us as a *Hint*. I would like to know how to come up with these integrating factors.

Here's some examples:

1) For the mean-reverting Ornstein-Uhlenbeck (OU) SDE dX_t = (m-X_t)dt+\sigma X_tdB(t), the appropriate integrating factor is e^t.

2) For the non-mean-reverting OU SDE dX_t = uX_tdt + \sigma dB_t, the integrating factor is e^{-ut}.

3) For the SDE dX_t = udt + \sigma X_t dB_t, the integrating factor is e^{-\sigma B_t + \frac12 \sigma^2 t}.
 
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Hi,
I suppose you are at the beginning of ODE course,so integrating factors will be discussed later on.
I hope you will find interest in the attached material here.
 
Last edited:
hedipaldi said:
Hi,
I suppose you are at the beginning of ODE course,so integrating factors will be discussed later on.
I hope you will find interest in the attached material here.

Thanks,

1) What attached material?
2) I'm at the end of a financial mathematics course (stochastic calculus). Integrating factors are provided to us and we will never learn how to discover them. I want to learn how to do this -- they aren't going to teach this to me.
 
The attached material concern ordinary differential equations.I suupose it is the same for stochastic.
 

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