Theory of Probability and Mathematical Statistics
Convergence of stochastic integrals to a continuous local martingale with conditionally independent increments
Andriy Yurachkivsky
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Abstract: For each T>0, let a tensor-valued stochastic process Y_T be defined by Y_T(t)=∫_0^tDZ_T(s)⊗ϑ_T(s), where Z_T is an R^d-valued locally square integrable martingale with respect to some filtration 𝔽_T and where ϑ_T is an R^d-valued 𝔽_T-predictable stochastic process such that ∫_0^t|ϑ_T(s)|^2Dtr(s)<∞ for all t. In this paper, conditions are found for the convergence (Y_T,)→(Y,Y), where Y is a continuous local martingale with conditionally independent increments given .
Keywords: Martingale, convergence, tensor
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