Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Gassiat, Paul"'
Autor:
Gassiat, Paul, Suciu, Florin
We consider the (sub-Riemannian type) control problem of finding a path going from an initial point $x$ to a target point $y$, by only moving in certain admissible directions. We assume that the corresponding vector fields satisfy the bracket-generat
Externí odkaz:
http://arxiv.org/abs/2407.11817
Autor:
Gassiat, Paul, Klose, Tom
Inspired by recent advances in singular SPDE theory, we use the Poincar\'e inequality on Wiener space to show that controlled complementary Young regularity is sufficient to obtain Gaussian rough paths lifts. This allows us to completely bypass assum
Externí odkaz:
http://arxiv.org/abs/2311.04312
The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them are (i) a regularization by noise
Externí odkaz:
http://arxiv.org/abs/2211.12099
Autor:
Gassiat, Paul, Mądry, Łukasz
We obtain well-posedness results for a class of ODE with a singular drift and additive fractional noise, whose right-hand-side involves some bounded variation terms depending on the solution. Examples of such equations are reflected equations, where
Externí odkaz:
http://arxiv.org/abs/2208.01961
Autor:
Gassiat, Paul
Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index $H \in (0,1/2)$. We obtain results on the rate of convergence for the
Externí odkaz:
http://arxiv.org/abs/2203.09298
Autor:
Gassiat, Paul, Seeger, Benjamin
We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a convexity ass
Externí odkaz:
http://arxiv.org/abs/2110.10337
Publikováno v:
In Journal of Functional Analysis 15 February 2024 286(4)
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise
Externí odkaz:
http://arxiv.org/abs/2009.08814
Autor:
Gassiat, Paul
We give an example of a reflected diffferential equation which may have infinitely many solutions if the driving signal is rough enough (e.g. of infinite $p$-variation, for some $p>2$). For this equation, we identify a sharp condition on the modulus
Externí odkaz:
http://arxiv.org/abs/2001.11914
We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of space-time subse
Externí odkaz:
http://arxiv.org/abs/1905.13174