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arXiv · 1407.6784

Algebraic Stochastic Calculus

Renaud Gauthier
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Abstract

We develop the foundations of Algebraic Stochastic Calculus, with an aim to replacing what is typically referred to as Stochastic Calculus by a purely categorical version thereof. We first give a sheaf theoretic reinterpretation of Probability Theory. We regard probability spaces (X, F, P) as Grothendieck sites (F, J_P) on which Brownian motions are defined via sheaves in symmetric monoidal infinity-categories. Due to the complex nature of such a formalism we are naturally led to considering a purely categorical, time independent formalism in which stochastic differential equations are replaced by studying problems in deformation theory.

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Renaud Gauthier. 2014-07-25. Algebraic Stochastic Calculus. https://arxiv.org/abs/1407.6784

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