In this section, we shall state and prove a result that implies Theorem 1.13 in the case where S is a d-dimensional continuous-path semimartingale. Note that Assumption (S-MART) will not be in force here; in particular, there can be more than one tr…

We developed a prediction-based randomized prescriptive algorithm that determines the probability of prescribing each treatment based on the predictions from an RLAD+K-NN model which takes into account both the high noise level and the nonlinearity …

The OPERA collaboration has reported evidence of superluminal neutrino propagationAdams:2011zb (). The CNGS beam, consisting of pulses of muon neutrinos with mean energy of 17.5 GeV and an energy spread extending beyond 50 GeV, travels about 730 km …

The “rank” of a vector space is the number of vectors in any basis of the space. In this setting, the vectors must not only span (or “generate”) the space, but also be linearly independent. The rank as defined and used in the previous sections have …

We start by mentioning (without proof) a special case of [3, Lemma A1.1], which will be used constantly throughout the proof of Theorem 1.3. Recall that a set B⊆L0+ is called bounded in probability if limℓ→∞supf∈BP[f>ℓ]=0.

In the course of the proofs below, we shall use the so-called Doob’s maximal identity, which we briefly recall for the reader’s convenience. If M is a continuous-path nonnegative local martingale on (Ω,F,P) such that P[limt→∞Mt=0]=1 holds, then, wit…

Theorem 7.2 of the seminal paper [9] establishes the semimartingale property of S under condition NFLVR for simple admissible strategies, coupled with a local boundedness assumption on S (always together with the càdlàg property and adaptedness). Th…