ERGODIC SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED TOPICS
Abstract
An L('2)-ergodic theorem is proved for solutions of stochastic differential equations driven by semimartingales. This is done using the semimartingale structure of solutions and local time techniques, since Markov solutions are no longer guaranteed. A strong stability result is proved as a consequence of the L('2)-ergodic theorem. A comparison between solutions of a stochastic differential equation and an ordinary differential equation is made and examples are given. Sufficient conditions for solutions to tend to infinity as time tends to infinity are obtained to make this comparison possible.
Degree
Ph.D.
Subject Area
Statistics
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