Contributions to Numerical Solution of Stochastic Differential Equations

Abstract: This thesis consists of four papers:

Paper I is an overview of recent techniques in strong numerical solutions of stochastic differential equations, driven by Wiener processes, that have appeared the last then 10 years, or so.

Paper II studies theoretical and numerical aspects of stochastic differential equations with so called volatility induced stationarity. While being of great importance in contemporary applications, these equations are particularly difficult from a numerical point of view, to the extent that most or even all standard numerical procedures fail.

Paper III develops numerical procedures for stochastic differential equations driven by Levy processes. A general scheme for stochastic Taylor expansions is developed, together with an analysis of convergence properties.

Paper IV shows how to reduce the common global Lipschitz condition for numerical procedures for stochastic differential equations, to a local Lipschitz condition.

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