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Inhomogeneous affine Volterra processes
Julia Ackermann, Thomas Kruse, Ludger Overbeck
We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an…
Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations
Christian Beck, Arnulf Jentzen, Thomas Kruse
The approximative calculation of iterated nested expectations is a recurring challenging problem in applications. Nested expectations appear, for example, in the numerical approxim…
Approximating exit times of continuous Markov processes
Thomas Kruse, Mikhail Urusov
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear wh…
Wasserstein convergence rates for random bit approximations of continuous Markov processes
Stefan Ankirchner, Thomas Kruse, Mikhail Urusov
We determine the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes. The scheme is based on the construction of coin tossi…
A functional limit theorem for coin tossing Markov chains
Stefan Ankirchner, Thomas Kruse, Mikhail Urusov
We prove a functional limit theorem for Markov chains that, in each step, move up or down by a possibly state dependent constant with probability , respectively. The theorem e…
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +2
For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort…