For the marketing term, see Diffusion of innovations.
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In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes. It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing.
A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability density function as a function of space and time is governed by a convection–diffusion equation.
statistics, diffusionprocesses are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusionprocess is stochastic...
A diffusion model consists of three major components: the forward process, the reverse process, and the sampling procedure. The goal of diffusion models...
Everett Rogers in his book Diffusion of Innovations, first published in 1962. Rogers argues that diffusion is the process by which an innovation is communicated...
concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random...
region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and...
Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. It is considered to be a part of the ongoing...
superseded by the more-efficient gas centrifuge process (enrichment factor 1.05 to 1.2). Gaseous diffusion was devised by Francis Simon and Nicholas Kurti...
In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without...
Anomalous diffusion is a diffusionprocess with a non-linear relationship between the mean squared displacement (MSD), ⟨ r 2 ( τ ) ⟩ {\displaystyle \langle...
Facilitated diffusion (also known as facilitated transport or passive-mediated transport) is the process of spontaneous passive transport (as opposed to...
data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusionprocess of molecules, mainly...
collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other...
reaction. The instability mechanism is unforeseen because a pure diffusionprocess would be anticipated to have a stabilizing influence on the system...
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections...
Markov process that models a population Diffusionprocess, a solution to a stochastic differential equation Empirical process, a stochastic process that...
Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of...
George M. (1956). The DiffusionProcess. Farm Foundation. pp. 111–121. doi:10.22004/ag.econ.17351. Savage, Robert L. (1985). "Diffusion Research Traditions...
are led to what are called jump processes. The other case leads to processes such as those "represented by diffusion and by Brownian motion; there it...
key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion processes...
options assumes that the underlying instrument follows a traditional diffusionprocess, with continuous, random movements at all scales, no matter how small...
statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe...
together. The diffusionprocess is described by the following three processes: surface diffusion grain boundary diffusion bulk diffusion This method enables...