Definition of the Stochastic Integral
In this chapter, we shall define stochastic integrals of the form ∫[0, t] X dM where M is a right continuous local L 2-martingale and X is a process satisfying certain measurability and integrability assumptions, such that the family of stochastic integrals (∫[0, t] X dM, t ∈ ℝ+ is a right continuous local L 2-martingale. For certain M and X, the integral can be defined path-by-path.
KeywordsContinuous Path Continuous Version Stochastic Integral Predictable Process Predictable Time
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