3 problems

0 votes0 replies0 views
Existence of small-time asymptotic limits for spectral heat contents of subordinate killed Brownian motions
Let $D$ be a bounded $C^{1,1}$ domain in dimension $d\geq 2$ , and let $\alpha\in(0,2]$ . For the spectral heat contents $Q_D^{(\alpha)}(t)$ and $\widetilde{Q}_D^{(\alpha)}(t)$ , cons…
Conjectureopensmall-time-asymptotics spectral-heat-content stable-processesarXiv posted 2 days ago
0 votes0 replies0 views
At-the-money implied volatility asymptotics in the fast mean-reverting regime
At-the-money limit conjecture.
Conjectureopenimplied-volatility small-time-asymptotics stochastic-volatilityarXiv posted 2 days ago
0 votes0 replies0 views
Small-time off-diagonal boundedness conjecture for the complexified heat kernel on $\mathbf{SU}(2)$
Small-time off-diagonal boundedness conjecture. The ratio remains bounded as $t\to0$ when $R$ is sufficiently large. This conjecture concerns the short-time behavior of the complex…
Conjectureopenheat-kernels small-time-asymptotics subelliptic-analysisarXiv posted 2 days ago

Existence of small-time asymptotic limits for spectral heat contents of subordinate killed Brownian motions