相关论文: BDG inequality for G-martingale
In this paper, we establish some new general Opial inequalities for Widder derivatives.
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator $g$ satisfies a weak…
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…
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its…
We prove Burkholder inequality using Bregman divergence.
In this article we derive some polynomial inequalities for Mertens functions.
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness…
A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.
The objective of this paper is to derive a representation of symmetric G-martingales as stochastic integrals with respect to the G-Brownian motion. For this end, we first study some extensions of stochastic calculus with respect to…
We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.
We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
The paper is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose $i$th component only depends on the $i$th row of the second unknown variable. Local and global…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
Sharp Moser-Trudinger type inequalities and their extremal functions play an important role in studying nonlinear PDEs and geometry. We establish a new sharp Moser-Trudinger type inequality in the upper half space in two dimensions and…
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…
We propose a new type SDE depending on the future distributions with all initial values, and establish the correspondence between this equation and the associated singular nonlinear PDE. Well-posedness and regularities are investigated.
We discuss BSDE with drivers containing nonlinearities of the type $p(y)|z|$ and $p(y)|z|^2$ with $p$ a polynomial of any degree. Sufficient conditions are given for existence and uniqueness of solutions as well as comparison results. We…
We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…