In this case, we consider pay-of functions e9783110329681_i2626.jpg e9783110329681_i2627.jpg, which are real-valued measurable functions assumed to satisfy condition e9783110329681_i2628.jpg, for some vector parameter e9783110329681_i2629.jpg with non-negative components.

Let us e9783110329681_i2630.jpg be the class of all stopping times τ0,n for the process Zn = (Yn

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