Related papers: Pathwise regularization by noise for semilinear SP…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely path. Any density peak moves along such a…
By using the Malliavin calculus and finite-jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic differential equations with noises containing a subordinate Brownian…
We delve deeper into the compelling regularizing effect of the Brownian-time Brownian motion density, $\KBtxy$, on the space-time-white-noise-driven stochastic integral equation we call BTBM SIE, which we recently introduced. In sharp…
We prove gradient estimates for transition Markov semigroups $(P_t)$ associated to SDEs driven by multiplicative Brownian noise having possibly unbounded $C^1$-coefficients, without requiring any monotonicity type condition. In particular,…
Motivated by applications to a manifold of semilinear and quasilinear stochastic partial differential equations (SPDEs) we establish the existence and uniqueness of strong solutions to coercive and locally monotone SPDEs driven by L\'{e}vy…
The interplay between concentration, flow, hydrodynamic interactions (HI), and topological interactions governing semidilute polymer dynamics in strong flows are challenging to characterize. Brownian dynamics (BD) simulations are…
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure $\mu$. We show that the average of regular enough test functions with respect to…
We prove the support recovery for a general class of linear and nonlinear evolutionary partial differential equation (PDE) identification from a single noisy trajectory using $\ell_1$ regularized Pseudo-Least Squares model~($\ell_1$-PsLS).…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter…
We investigate the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like H{\"o}rmander structure (i.e. a non-degeneracy…
In this article, we present a general methodology for control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…
In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idealized model of a diffusion where approximations such as…
In this paper we aim at generalizing the results of A. K. Zvonkin and A. Y. Veretennikov on the construction of unique strong solutions of stochastic differential equations with singular drift vector field and additive noise in the…
In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In the majority of these results it is assumed that the drift…