Uniqueness in cauchy problems for diffusive real-valued strict local martingales
Çetin, U.
& Larsen, K.
(2023).
Uniqueness in cauchy problems for diffusive real-valued strict local martingales.
Transactions of the American Mathematical Society Series B,
10(13), 381-406.
https://doi.org/10.1090/btran/141
& Larsen, K.
(2023).
Uniqueness in cauchy problems for diffusive real-valued strict local martingales.
Transactions of the American Mathematical Society Series B,
10(13), 381-406.
https://doi.org/10.1090/btran/141
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 1 2 \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.
