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In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…
We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
The existence of strong solutions to general class of strongly coupled parabolic systems will be discussed. These systems can be degenerate or singular as boundedness of theirs solutions are unavailable and not assummed. The results greatly…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
We consider systems of stochastic differential equations of the form \[ \d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for $i=1,\dots,d$ with continuous, bounded and non-degenerate coefficients. Here $Z_t^1,\dots,Z_t^d$ are independent…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…
Recently the primal-dual method of multipliers (PDMM), a novel distributed optimization method, was proposed for solving a general class of decomposable convex optimizations over graphic models. In this work, we first study the convergence…
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient…
Motivated by applications to stochastic differential equations, an extension of H\"{o}rmander's hypoellipticity theorem is proved for second-order degenerate elliptic operators with non-smooth coefficients. The main results are established…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
This paper develops techniques to study the number of descents in random permutations via martingales. We relax an assumption in the Berry-Esseen theorem of Bolthausen (1982) to extend the theorem's scope to martingale differences of…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduced, boundary representations for…