In this talk we introduce a family of numerical approximations for the stochastic differentialequations (SDEs) with, possibly, no-globally Lipschitz coefficients. We show that for a given Lyapunovfunction V : R → [1,∞) we can construct a suitably tamed Euler scheme that preserves so calledV-stability property of the original SDEs without imposing any restrictions on the time dis...

"Monte Carlo simulation" in the context of option pricing refers to a set of techniques to generate underlying values–typically stock prices or interest rates–over time. Typically the dynamics of these stock prices and interest rates are assumed to be driven by a continuous-time stochastic process. Simulation, however, is done at discrete time steps. Hence, the …rst step in any simulation schem...

In the present work we propose and analyze a fully-coupled virtual element method of high order for solving two dimensional nonstationary Boussinesq system in terms stream-function temperature fields. The discretization spatial variables is based on coupling C1- C0-conforming approaches, while backward Euler scheme employed temporal variable. Well-posedness unconditional stability fully-discret...

Abstract In this paper, we analyse a proximal method based on the idea of forward–backward splitting for sampling from distributions with densities that are not necessarily smooth. particular, study non-asymptotic properties Euler–Maruyama discretization Langevin equation, where envelope is used to deal non-smooth part dynamics. An advantage envelope, when compared widely-used Moreu–Yoshida one...

We present an algorithm for solving stochastic heat equations, whose key ingredient is a non-uniform time discretization of the driving Brownian motion W . For this algorithm we derive an error bound in terms of its number of evaluations of onedimensional components of W . The rate of convergence depends on the spatial dimension of the heat equation and on the decay of the eigenfunctions of the...

This paper is concerned with the application of transient complete flux scheme to a radio frequency discharge model in one-dimensional geometry. The and exponential difference are used discretize plasma fluxes space. Temporal discretization performed by using implicit Euler method 2-step backward differentiation formula first second orders. Numerical experiments carried out evaluate order level...

For a linear-quadratic state constrained optimal control problem, it is proved in [11] that under an independence condition for the active constraints, the optimal control is Lipschitz continuous. We now give a new proof of this result based on an analysis of the Euler discretization given in [9]. There we exploit the Lipschitz continuity of the control to estimate the error in the Euler discre...

In this paper it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an event-capturing, or time-stepping a...

In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black–Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, class of finite volume (FVM) is proposed spatial discretization, coupled with backward Euler Crank–Nicolson schemes are employed time stepping partial differential equatio...

We propose and analyze two locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity. One is a high-order scheme, the other low-order scheme. For time discretization, we use backward Euler The proposed are well-posed, optimal error estimates of all unknowns obtained fully discrete solutions. generic constants uniformly bounded as Lamé coefficient ? tends ...