On the Resolution of Some Itô Diffusions by the Heat Equation

Sameerah Jamal

International Journal of Differential Equations, 2026, vol. 2026, 1-8

Abstract: We consider a class of partial differential equations that arise from one-dimensional generalized square root problems, featuring drift and diffusion. In particular, we investigate models whereby a diffusion coefficient is described by a power law. Our central aim is to discover coordinate transformations that convert these equations to the heat equation. This is realized by obtaining a necessary and sufficient condition for the underlying drift function. As a direct consequence, we prove how to recover transition probability densities that satisfy a Cauchy problem involving the Dirac measure.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:4328746

DOI: 10.1155/ijde/4328746

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