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# Analysis of a splitting method for stochastic balance laws

Abstract: We analyze a semi-discrete splitting method for conservation laws driven by a semilinear noise term. Making use of fractional $BV$ estimates, we show that the splitting method produces a compact sequence of approximate solutions converging to the exact solution, as the time step $\Delta t \to 0$. Under the assumption of a homogenous noise function, and thus the availability of $BV$ estimates, we provide an $L^1$ error estimate. Bringing into play a generalization of Kružkov's entropy condition, permitting the “Kružkov constants” to be Malliavin differentiable random variables, we establish an $L^1$ convergence rate of order $\frac13$ in $\Delta t$.

Paper:
Available as PDF (478 Kbytes).
Author(s):
Kenneth H. Karlsen
Erlend B. Storrøsten