Paul Levy constructed this as the uniform limit of a series of successive approximations which interpolate linearly between random variables on the dyadic rationals, so that the joint distribution at each stage is the same as in the limit.
Given this function as input, the Loewner equation gives the family of random planar curves known as the Schramm-Loewner evolution. Paul Levy constructed this as the uniform limit of a series of successive approximations which interpolate linearly between random variables on the dyadic rationals, so that the joint distribution at each stage is the same as in the limit. As a random process in the plane it is nowhere differentiable almost surely, and its boundary has fractal dimension 4/3. It itself has dimension 2, the same as a space-filling curve or random walk.  It is defined as an almost surely continuous stochastic process with independent increments normally distributed with expectation zero and variance h given time interval h. For 10 points, name this process, also termed a Wiener process, used to model stock market prices in the Black-Scholes model as well as the diffusion of particles in a fluid.
Given this function as input, the Loewner equation gives the family of random planar curves known as the Schramm-Loewner evolution.
{Brownian motion} (accept {Wiener process} before mentioned)