Uniqueness in Cauchy problems for diffusive real-valued strict local martingales

Çetin, Umut; Larsen, Kasper

doi:10.1090/btran/141

Uniqueness in Cauchy problems for diffusive real-valued strict local martingales
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by Umut Çetin and Kasper Larsen

Trans. Amer. Math. Soc. Ser. B 10 (2023), 381-406

DOI: https://doi.org/10.1090/btran/141

Published electronically: March 6, 2023

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Abstract:

For a real-valued one dimensional diffusive strict local martingale, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local $\frac 12$-Hölder condition. Under the weaker Engelbert-Schmidt conditions, we provide a set in which the Cauchy problem has a unique weak solution. We exemplify our results using quadratic normal volatility models and the two dimensional Bessel process.

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