Published on:

14 May 2024

Primary Category:

Probability

Paper Authors:

Kevin Hu,

Kavita Ramanan,

William Salkeld

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A fundamental martingale allows change of measure for fractional Brownian motion

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This leads to a Girsanov theorem for systems of equations

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Weak existence and uniqueness hold for countable systems

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The law forms a 2-Markov Random Field on path space

Locally interacting stochastic differential equations driven by fractional Brownian motion

We consider collections of stochastic differential equations indexed by a graph, with each equation driven by fractional Brownian motion. The drift term in each SDE interacts only with the SDEs corresponding to neighboring vertices. We derive a fundamental martingale for the driving noise which allows a Girsanov-type change of measure. This leads to weak existence, uniqueness, and a 2-Markov Random Field property for the laws of these interacting systems.

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