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We prove that, under the H\"ormander criterion on an It\^{o} process, all its martingale observables are smooth.
Théorèmes d’unicité pour l’équation de la chaleur
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Hypoelliptic second-order differential equations
L. Hörmander · 1967
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Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés
J.-M. Bony · 1969
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On degenerate elliptic-parabolic operators of second order and their associated diffusions
D. Stroock and S. R. S. Varadhan · 1972
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Functional analysis
W. Rudin · 1973
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Calcul Stochastique et Problèmes de Martingales
J. Jacod · 1979
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When is a stochastic integral a time change of a diffusion?
B. Øksendal · 1990
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A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
S. L. Heston · 1993
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Methods of Mathematical Finance
I. Karatzas, S.E. Shreve · 1998
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
S. Smirnov · 2001
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Handbook of Brownian Motion — Facts and Formulae (2nd ed.). Springer, 2002
A. N. Borodin and P. Salminen · 2002
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Stochastic Differential Equations (6th ed.)
B. Øksendal · 2003
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Conformal invariance of planar loop-erased random walks and uniform spanning trees
G. F. Lawler, O. Schramm, and W. Werner · 2004
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Conformally invariant processes in the plane
G. F. Lawler · 2005
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Basic properties of SLE
S. Rohde and O. Schramm · 2005
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The Malliavin calculus and related topics
D. Nualart · 2006
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Partial differential equations for probabilists
D. W. Stroock · 2008
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The scaling limits of planar LERW in finitely connected domains
D. Zhan · 2008
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Hypocoercivity
C. Villaini · 2009
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On optimal arbitrage
D. Fernholz and I. Karatzas · 2010
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Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations
K. Kobayashi · 2011
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Degenerate Diffusion Operators Arising in Population Biology
C. L. Epstein and R. Mazzeo · 2013
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Ising interfaces and free boundary conditions
C. Hongler, and K. Kytölä · 2013
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Electr. J. Probab. 25, 2020
A. Karrila. UST branches, martingales, and multiple SLE(2) · 2020
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Boundary correlations in planar LERW and UST
A. Karrila, K. Kytölä, and E. Peltola · 2020
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Hypergeometric SLE: Conformal Markov Characterization and Applications
H. Wu · 2020
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A Feynman-Kac formula for a degenerate Kolmogorov backward equation
B. van Doren · 2021
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A new computation of pairing probabilities in several multiple-curve models
— · 2022
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Crossing Probabilities of Multiple Ising Interfaces
E. Peltola and H. Wu · 2023
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E. Azmoodeh, T. Sottinen, L. Viitasaari, and A. Yazigi · 2014
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Convergence of Ising interfaces to Schramm’s SLE curves
D. Chelkak, H. Duminil-Copin, C. Hongler, A. Kemppainen, and S. Smirnov · 2014
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SLE and Virasoro representations: localization
Julien Dubédat · 2015
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A solution space for a system of null-state partial differential equations, Part I
S. M. Flores and P. Kleban · 2015
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A solution space for a system of null-state partial differential equations, Part II
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Optimal Regularity of a Degenerate Elliptic Equation
X. Wang and J. Zhang · 2023
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Multiple SLEs for κ ∈ ( 0 , 8 ) \kappa\in(0,8) : Coulomb gas integrals and pure partition functions
Y. Feng, M. Liu, E. Peltola, and H. Wu · 2024
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Connection probabilities of multiple FK-Ising interfaces
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Radial BPZ equations and partition functions of FK-Ising interfaces conditional on one-arm event
Y. Feng and H. Wu · 2024
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Necessary and sufficient conditions for continuity of hypercontractive processes and fields
P. Nummi and L. Viitasaari · 2024
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Existence and Uniqueness of Nonsimple Multiple SLE
D. Zhan · 2024
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Monte Carlo Methods for Partial Differential Equations With Applications to Electronic Design Automation
W. Yu and M. Mascagni · 2024
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Conformal welding of quantum disks and multiple SLE: the non-simple case
M. Ang, N. Holden, X. Sun, and P. Yu · 2025
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On the mathematical foundations of diffusion Monte Carlo
M. Caffarel, P. Del Moral, and L. de Montella · 2025
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Multiradial SLE with spiral: resampling property and boundary perturbation
C. Huang, E. Peltola, and H. Wu · 2025
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Planar UST branches and c = − 2 c=-2 degenerate boundary correlations
A. Karrila, A. Lafay, E. Peltola, and J. Roussillon · 2025
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