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A Lyapunov-tamed Euler method for singular SDEs
Tim Johnston, Pierre Monmarché
Many applications, such as systems of interacting particles in physics, require the simulation of diffusion processes with singular coefficients. Standard Euler schemes are then no…
A Tamed Euler Scheme for SDEs with Non-Locally Integrable Drift Coefficient
Tim Johnston, Sotirios Sabanis
In this article we show that for SDEs with a drift coefficient that is non-locally integrable, one may define a tamed Euler scheme that converges in at rate to the true…
Taming the Interacting Particle Langevin Algorithm: The Superlinear case
Tim Johnston, Nikolaos Makras, Sotirios Sabanis
Recent advances in stochastic optimization have yielded the interacting particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to effi…
Convergence Of The Unadjusted Langevin Algorithm For Discontinuous Gradients
Tim Johnston, Sotirios Sabanis
We demonstrate that for strongly log-convex densities whose potentials are discontinuous on manifolds, the ULA algorithm converges with stepsize bias of order in Wasserstein-…
Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
Tim Johnston, Iosif Lytras, Sotirios Sabanis
In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algor…
A Strongly Monotonic Polygonal Euler Scheme
Tim Johnston, Sotirios Sabanis
In recent years tamed schemes have become an important technique for simulating SDEs and SPDEs whose continuous coefficients display superlinear growth. The taming method, which in…