A weak Local Linearization scheme for stochastic differential equations with multiplicative noise
For researchers in numerical SDEs, this provides a new weak scheme with proven convergence, though it is incremental as it extends an existing Local Linearization approach to multiplicative noise.
The paper introduces a weak Local Linearization scheme for SDEs with multiplicative noise, achieving a specific convergence rate (not numerically specified in abstract) and demonstrates its performance via simulations.
In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the piecewise linear SDE that results from the Local Linearization strategy. The weak numerical scheme is then defined as a sequence of random vectors whose first moments coincide with those of the piecewise linear SDE on the time discretization. The rate of convergence is derived and numerical simulations are presented for illustrating the performance of the scheme.