Related papers: On Quadratic BSDEs with Final Condition in L2
We consider a class of multi-dimensional BSDEs on a finite time horizon (containing in particular Lipschitzian-quadratic BSDEs), whose terminal values are bounded as well as their corresponding Malliavin derivatives. We prove two results.…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, $L^p (p>1)$ solutions and…
We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in…
The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…
A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…
In this paper, we study a class of Quadratic Backward Stochastic Differential Equations (QBSDE in short) with jumps and unbounded terminal condition. We extend the class of quadratic semimartingales introduced by Barrieu and El Karoui…
We prove a general theorem that the $L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solution of an infinite horizon backward doubly stochastic differential equation, if exists,…
In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator, which is of…
Semilinear stochastic partial differential equations on bounded domains $\mathscr{D}$ are considered. The semilinear term may have arbitrary polynomial growth as long as it is continuous and monotone except perhaps near the origin. Typical…
In this paper we investigate the asymptotic stability of a fourth-order PDE with a fading memory forcing term and boundary conditions arising from a flexible robotics model. We carry on our study by using an abstract formulation of the…
This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between $L_{\rho}^2({\mathbb{R}^{d}};{\mathbb{R}^{1}}) \otimes…
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex…
In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted…
In this paper, we study the well-posedness and regularity of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear, locally Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is the fact…