What type of study is this?

This is a Quantitative Study study.

October 1, 2025Open Access

The area of spheres in the Brownian plane

Puntos clave

The area of spheres in the Brownian plane has continuously differentiable sample paths, establishing a smooth relationship with radius.
A stochastic differential equation governs the behavior of this area process, indicating a complex interaction with its derivative.
The derived process, along with its derivative, forms a time-homogeneous Markov pair, highlighting their probabilistic dependencies over time.
Implications suggest that understanding this Markov relationship can enhance applications in stochastic models and financial mathematics.

Resumen

We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and its derivative is time-homogeneous Markov and satisfies an explicit stochastic differential equation.

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Cite This Study

Jean-François Le Gall (Tue,) studied this question.

synapsesocial.com/papers/68dd91cbfe798ba2fc4986c9 https://doi.org/https://doi.org/10.48550/arxiv.2504.15860

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