相关论文: Density analysis of BSDEs
Using probabilistic methods, we establish a-priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity which has quadratic growth in the…
We study a class of stochastic differential equations driven by a possibly tempered L{\'e}vy process, under mild conditions on the coefficients. We prove the well-posedness of the associated martingale problem as well as the existence of…
We consider a solution to a generic Markovian jump diffusion and show that for positive times the law of the solution process has a smooth density with respect to Lebesgue measure under a uniform version of Hoermander's conditions. Unlike…
In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise,…
We study the sensitivity of the densities of some Kolmogorov like degenerate diffusion processes with respect to a perturbation of the coefficients of the non-degenerate component. Under suitable (quite sharp) assumptions we quantify how…
In this paper the existence of a smooth density is proved for the solution of an SDE, with locally Lipschitz coefficients and semi-monotone drift, under H\"ormander condition. We prove the nondegeneracy condition for the solution of the…
In this paper, we study the relation between the smallest $g$-supersolution of constraint backward stochastic differential equation and viscosity solution of constraint semilineare parabolic PDE, i.e. variation inequalities. And we get an…
We study multidimensional backward stochastic differential equations (BSDEs) which cover the logarithmic nonlinearity u log u. More precisely, we establish the existence and uniqueness as well as the stability of p-integrable solutions (p >…
This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the $m$-Hessian measure that belongs to $L^q$, for $q\leq\frac nm$.
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the…
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject…
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
We generalize the theory of periodic homogenization for multidimensional SDEs with additive Brownian and stable L\'evy noise for $\alpha\in (1,2)$ to the setting of singular periodic Besov drifts of regularity $\beta\in ((2-2\alpha)/3,0)$…
Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217,…
We study the existence of minimal supersolutions of BSDEs under a family of mutually singular probability measures. We consider generators that are jointly lower semicontinuous, positive, and either convex in the control variable and…
In this paper, we investigate the well-posedness of bounded and unbounded solutions for reflected backward stochastic differential equations (RBSDEs) and backward stochastic differential equations (BSDEs). The generators of these equations…
In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with…
We show removability of half-line singularities for viscosity solutions of fully nonlinear elliptic PDEs which have classical density and a Jacobi inequality. An example of such a PDE is the Monge-Amp\`ere equation, and the original proof…