89 citations · 251 across the 12 of their papers we have counts for
12 papers
An energy-based deep splitting method for the nonlinear filtering problem
Kasper Bågmark, Adam Andersson, Stig Larsson
The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep split…
Convergence of a robust deep FBSDE method for stochastic control
Kristoffer Andersson, Adam Andersson, Cornelis W. Oosterlee
In this paper, we propose a deep learning based numerical scheme for strongly coupled FBSDEs, stemming from stochastic control. It is a modification of the deep BSDE method in whic…
Finite element approximation of Lyapunov equations related to parabolic stochastic PDEs
Adam Andersson, Annika Lang, Andreas Petersson +1
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicat…
Malliavin regularity and weak approximation of semilinear SPDE with Lévy noise
Adam Andersson, Felix Lindner
We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable Lévy…
Poisson Malliavin calculus in Hilbert space with an application to SPDE
Adam Andersson, Felix Lindner
In this paper we introduce a Hilbert space-valued Malliavin calculus for Poisson random measures. It is solely based on elementary principles from the theory of point processes and…
Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces
Adam Andersson, Mario Hefter, Arnulf Jentzen +1
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diff…
On the differentiability of solutions of stochastic evolution equations with respect to their initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan +1
In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the…
Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan
In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the…
Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
Adam Andersson, Raphael Kruse
In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to…
Weak error analysis for semilinear stochastic Volterra equations with additive noise
Adam Andersson, Mihály Kovács, Stig Larsson
We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian nois…
Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE
Adam Andersson, Raphael Kruse, Stig Larsson
We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a B…
Weak convergence for a spatial approximation of the nonlinear stochastic heat equation
Adam Andersson, Stig Larsson
We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is…