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Bernoulli representation 1boundary behavior 1conditional density 1diffusion processes 1fokker-planck equation 1martingales 1pathwise filtering 1rough Heston 1rough volatility 1stochastic calculus 1stochastic volatility 1

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math.PR2026

On the boundaries, asymptotic law and Bernoulli-Doob representation of homogeneous bounded martingales

Damiano Brigo, Frédéric Vrins, Frédéric Vrins

The paper shows that any bounded homogeneous diffusion martingale on a finite interval can be represented as the conditional expectation of a Bernoulli variable (a Bernoulli-Doob m…