8 citations · 53 across the 24 of their papers we have counts for
12 papers · 1 filter
On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models
Alexander Kalinin, Thilo Meyer-Brandis, Annika Steibel
We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-…
Regularity of Solutions of Mean-Field -SDEs
Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis
We study regularity properties of the unique solution of a mean-field -SDE. More precisely, we consider a mean-field -SDE with square-integrable random initial condition and…
Mean-Field SDEs driven by -Brownian Motion
Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis
We extend the notion of mean-field SDEs to SDEs driven by -Brownian motion. More precisely, we consider a -SDE where the coefficients depend not only on time and the current…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Li…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic c…
McKean-Vlasov equations on infinite-dimensional Hilbert spaces with irregular drift and additive fractional noise
Martin Bauer, Thilo Meyer-Brandis
This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dim…
Strong Solutions of Mean-Field SDEs with irregular expectation functional in the drift
Martin Bauer, Thilo Meyer-Brandis
We analyze multi-dimensional mean-field stochastic differential equations where the drift depends on the law in form of a Lebesgue integral with respect to the pushforward measure…
Existence and Regularity of Solutions to Multi-Dimensional Mean-Field Stochastic Differential Equations with Irregular Drift
Martin Bauer, Thilo Meyer-Brandis
We examine existence and uniqueness of strong solutions of multi-dimensional mean-field stochastic differential equations with irregular drift coefficients. Furthermore, we establi…
Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise
David Baños, Martin Bauer, Thilo Meyer-Brandis +1
In this paper we aim at generalizing the results of A. K. Zvonkin and A. Y. Veretennikov on the construction of unique strong solutions of stochastic differential equations with si…
Strong Solutions of Mean-Field Stochastic Differential Equations with irregular drift
Martin Bauer, Thilo Meyer-Brandis, Frank Proske
We investigate existence and uniqueness of strong solutions of mean-field stochastic differential equations with irregular drift coefficients. Our direct construction of strong sol…
Bootstrap percolation in directed and inhomogeneous random graphs
Nils Detering, Thilo Meyer-Brandis, Konstantinos Panagiotou
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual thresh…
Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle
David R. Baños, Sindre Duedahl, Thilo Meyer-Brandis +1
In this paper we aim at employing a compactness criterion of Da Prato, Malliavin, Nualart for square integrable Brownian functionals to construct unique strong solutions of SDE's u…