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A Quickest Detection Problem With An Observation Cost

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Geometric Brownian motion

A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model.

Acid strength

Acid strength is the tendency of an acid, symbolised by the chemical formula HA, to dissociate into a proton, H+, and an anion, A-. The dissociation of a strong acid in solution is effectively complete, except in its most concentrated solutions. HA -> H+ + A- Examples of strong acids are hydrochloric acid (HCl), perchloric acid (HClO4), nitric acid (HNO3) and sulfuric acid (H2SO4). A weak acid is only partially dissociated, with both the undissociated acid and its dissociation products being present, in solution, in equilibrium with each other.

Sound change

A sound change, in historical linguistics, is a change in the pronunciation of a language. A sound change can involve the replacement of one speech sound (or, more generally, one phonetic feature value) by a different one (called phonetic change) or a more general change to the speech sounds that exist (phonological change), such as the merger of two sounds or the creation of a new sound. A sound change can eliminate the affected sound, or a new sound can be added.

Language change

Language change is variation over time in a language's features. It is studied in several subfields of linguistics: historical linguistics, sociolinguistics, and evolutionary linguistics. Traditional theories of historical linguistics identify three main types of change: systematic change in the pronunciation of phonemes, or sound change; borrowing, in which features of a language or dialect are altered as a result of influence from another language or dialect; and analogical change, in which the shape or grammatical behavior of a word is altered to more closely resemble that of another word.