Stochastic Integration in Banach Spaces pp 87-103 | Cite as

# Stochastic Integral Equations in Banach Spaces

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## Abstract

In this chapter, we first study the solutions of stochastic differential equations with non-Markovian Lipschitz condition and growth condition. In this case the drift and noise coefficients \(a(t,Z)\) and \(f(t,x,Z)\), being non-anticipating, depend on the path of the solution \(Z\) \(=(Z_t)_{t\in [0,T]}\). This is done by defining the equation on a probability space with \(\Omega :=\) \(D(\mathbb {R}_+,E)\), the space of càdlàg functions on \(\mathbb {R}_+ \rightarrow E\), and with the \(\sigma \)-algebra generated by the cylinder sets of \(D(\mathbb {R}_+,E)\), where \(E\) is a separable Banach space.

## Keywords

Banach Space Probability Space Stochastic Differential Equation Lipschitz Condition Markov Property
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## Copyright information

© Springer International Publishing Switzerland 2015