Mathematical Sciences: Stochastic Differential Equations

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The principal investigator will conduct research in several areas of stochastic differential equations. This area of stochastic calculus is a field within probability theory which has impact on several disciplines: electrical engineering, mathematical physics, finance and economics. In particular, the investigator will study weak convergence of stochastic integrals and stochastic differential equations, with investigations into numerical schemes for approximating solutions of stochastic differential equations driven by general semi-martingales. In addition he will study a new type of forward-backward equation which arose in finance theory. Finally, he has proposed a new type of Stratonovich stochastic differential equation for general semimartingales which allows approximation of the jumping differentials by continuous processes in a Wong-Zakai manner. The principal investigator will conduct research in several areas of stochastic differential equations. This area of stochastic calculus is a field within probability theory which has impact on several disciplines: electrical engineering, mathematical physics, finance and economics.