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Lipschitz Stochastic Differential Equations

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Stochastic Calculus and Applications

Part of the book series: Probability and Its Applications ((PA))

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Abstract

As is now usual, all (in)equalities in this chapter should be read as ‘up to an evanescent set’, unless otherwise specified, martingales are càdlàg and we assume we have a filtered probability space satisfying the usual conditions. In this chapter, we consider stochastic differential equations (SDEs), that is, m-dimensional processes X satisfying an equation of the form

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Notes

  1. 1.

    Here and elsewhere, when stating that an equation has a unique solution, we mean both that a solution exists and that the solution is unique.

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  1. Mathematical Institute, University of Oxford, Oxford, UK

    Samuel N. Cohen

  2. School of Mathematics, University of Adelaide, Adelaide, Australia

    Robert J. Elliott

  3. Haskayne School of Business, University of Calgary, Calgary, Canada

    Robert J. Elliott

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Cohen, S.N., Elliott, R.J. (2015). Lipschitz Stochastic Differential Equations. In: Stochastic Calculus and Applications. Probability and Its Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-2867-5_16

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