Published · Annales de l’Institut Henri Poincaré / C, 33 (2016) 4, pp. 933-963. We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space-time transport noise and affine-linear noise driven by a geometric p-rough path. In particular,…
Published · Communications in mathematical physics, 335 (2015) 1, pp. 309-344. We prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space-time noise, corresponding to the Bak-Tang-Wiesenfeld model for self-organized criticality. This solves a problem posed and left…
Published · The annals of probability, 44 (2016) 1, pp. 684-738. We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and…
It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than Brownian…
We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions comes from recent work of Hairer [CPAM,2011].…
Published · SIAM journal on mathematical analysis, 45 (2013) 5, pp. 2734-2766. We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies…
Published · Journal of dynamics and differential equations, 25 (2013) 1, pp. 121-157. We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only…
Published · Journal de mathématiques pures et appliquées, 101 (2014) 6, pp. 789-827. We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular…
Published · Journal of differential equations, 255 (2013) 3, pp. 524-559. The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational…
Published · The annals of probability, 42 (2014) 2, pp. 818-864. Unique existence of solutions to porous media equations driven by continuous linear multiplicative space-time rough signals is proven for initial data in $L^1(\mathcal {O})$ on bounded domains $\mathcal {O}$. The generation of…
Published · Journal of functional analysis, 263 (2012) 8, pp. 2355-2383. Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies…
Published · Journal of differential equations, 251 (2011) 4-5, pp. 1225-1253. The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE,…
