Convergence of the stochastic Euler scheme for locally Lipschitz coefficients

Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case of superlinearly growing coefficients, however, has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth.Comment: Published at http://www.springerlink.com/content/g076w80730811vv3 in the Foundations of Computational Mathematics 201

Smoothness of Wave Functions in Thermal Equilibrium

none2TUMULKA R.; P. ZANGHI'Tumulka, R.; Zanghi', Pierantoni

Well-posedness and invariant measures for HJM models with deterministic volatility and Levy noise

We give sufficient conditions for the existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Levy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.American style derivative securities, Continuous time finance, Control of stochastic systems, Differential equations, Term structure,