Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:
Exponential tilting
In Monte Carlo Estimation, exponential tilting (ET), exponential twisting, or exponential change of measure (ECM) is a distribution shifting technique commonly used in rare-event simulation, and rejection and importance sampling in particular. Exponential tilting is also used in Esscher tilting, an indirect Edgeworth approximation technique. The earliest formalization of ECM is often attributed to Esscher with its use in importance sampling being attributed to David Siegmund. ET is known as the Esscher transform in mathematical finance and is used in such contexts as insurance futures pricing.