Abstract
The Brownian motion is nowhere differentiable with probability 1 (see the Paley–Wiener–Zygmund theorem in Chapter 2); it therefore makes not much sense to calculate integrals of the type that appear in the solution of Langevin’s equation (1.27).
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Schuss, Z. (2010). Itô Integration and Calculus. In: Theory and Applications of Stochastic Processes. Applied Mathematical Sciences, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1605-1_3
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DOI: https://doi.org/10.1007/978-1-4419-1605-1_3
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