subordinator

A subordinator is a term used in two distinct fields to denote related but separate concepts tied to subordination. In linguistics, a subordinator is a word or morpheme that introduces a subordinate (dependent) clause. These subordinators, often called subordinating conjunctions, connect a dependent clause to a main clause and indicate relationships such as cause, time, condition, contrast, or purpose. Common examples in English include because, since, if, when, although, while, before, and after. Subordinators differ from coordinating conjunctions, which join elements of equal syntactic rank, and from complementizers that introduce embedded clauses in some grammars.

In probability theory, a subordinator is a non-decreasing Lévy process with càdlàg paths that starts at zero. It serves as a random increasing time change for other stochastic processes. A subordinator is characterized by its Laplace exponent φ, with the relation E[exp(-λ S_t)] = exp(-t φ(λ)). The increments are stationary and independent, and jumps occur only in the positive direction. Notable examples include the gamma process, the inverse Gaussian process, and the stable subordinator. Subordinators are used to construct time-changed processes Y_t = X_{S_t}, enabling models of phenomena with heavy-tailed waiting times and anomalous diffusion. The inverse subordinator T(s) = inf{t: S_t > s} is used to model retarded dynamics and can yield non-Markovian behavior.

Overall, while the term shares a root concept of subordination, its precise meaning depends on the discipline: a linguistic connector that introduces dependent clauses, or a stochastic process that models random, non-decreasing time changes.