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I have noticed most of the books about stochastic calculus are targeted fo finance and derivatives. Are there any other areas outside finance where stochastic calculus is applicable?

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    $\begingroup$ Do a search on missle control systems and other areas of automated control or where you require control over multidimensional Random fluctuations. $\endgroup$
    – Chinny84
    Jun 17, 2015 at 21:31
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    $\begingroup$ Stochastic processes appear a lot in nature, especially in Quantum Mechanics. Have a look at the Stochastic Schrodinger Equation. They also appear in Thermodynamics and kinetic theory (cf. the Wiener process) $\endgroup$ Jun 17, 2015 at 21:32
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    $\begingroup$ The Feynman-Kac equations (Circa, 1949) precede derivatives' pricing theory and the corresponding use of stochastic calculus in financial engineering. $\endgroup$
    – Mark Viola
    Jun 17, 2015 at 21:39
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    $\begingroup$ Relevant: math.stackexchange.com/questions/1170582/… $\endgroup$
    – Math1000
    Jun 17, 2015 at 22:47

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Stochastic calculus is a huge area in physics, engineering, and pure math.

What is a really huge topic in research right now are SPDEs. Stochastic partial differential equations. Take your favorite PDE and add some noise to it. Now you have a SPDE. These equations have numerous mathematical challenges, such as issues of roughness and defining solutions, but also have great applications in fluid mechanics, thermodynamics, quantum dynamics, whatever PDE you're interested in!

Additionally, another thing that is only SDEs and stochastic calculus is Wright Fischer diffusion. There is an SDE that explains the distribution of alleles in a population. This is a connection to biology.

Really, anything with "noise" in it, might require some stochastic calculus!

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