Related papers: Approximation analysis for weak solutions of stoch…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…
The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but, to the best of our knowledge, none of them prove strong or…
We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term…
We discuss regular and weak solutions to rough partial differential equations (RPDEs), thereby providing a (rough path-)wise view on important classes of SPDEs. In contrast to many previous works on RPDEs, our definition gives honest…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not…
This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a…
One introduces a new variational concept of solution for the stochastic differential equation $dX+A(t)X\,dt+\lambda X\,dt=X\,dW,$ $t\in(0,T)$; $X(0)=x$ in a real Hilbert space where $A(t)=\partial\varphi(t)$, $t\in(0,T)$, is a maximal…
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate. As an application, the existence and uniqueness of solution to the…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…
This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than processes in the generalized sense. We consider a first order…