Stopped processes and Doob's optional sampling theorem

The Optional Sampling Theorem for Partially Ordered Time Processes and Multiparameter Stochastic Calculus

Optional pragmatic processes or optional covert linguistic structure?*

The starting point for this paper is an asymmetry between overt linguistic indexicals and (alleged) covert indexicals. It has been proposed that the problem can be solved by making covert indexicals optional (Martí 2006) and that this provides a much better (linguistically respectable) account of the key phenomena than one that advocates an optional process of free (not linguistically mandated)...

Stopped diffusion processes: boundary corrections and overshoot

For a stopped diffusion process in a multidimensional time-dependent domain D, we propose and analyse a new procedure consisting in simulating the process with an Euler scheme with step size ∆ and stopping it at discrete times (i∆)i∈N∗ in a modified domain, whose boundary has been appropriately shifted. The shift is locally in the direction of the inward normal n(t, x) at any point (t, x) on th...

The Sampling Theorem and the Bandpass Theorem

Boas' Formula and Sampling Theorem

In 1937, Boas gave a smart proof for an extension of the Bernstein theorem for trigonometric series. It is the purpose of the present note (i) to point out that a formula which Boas used in the proof is related with the Shannon sampling theorem; (ii) to present a generalized Parseval formula, which is suggested by the Boas’ formula; and (iii) to show that this provides a very smart derivation o...