potential in a viscous fluid. Itô diffusions are named after the Japanese mathematician Kiyosi Itô. A (time-homogeneous) Itô diffusion in n-dimensional Euclidean...

variable formula known as Itô's lemma (also known as the Itô formula). Itô also made contributions to the study of diffusion processes on manifolds, known...

equation Itô calculus Fokker–Planck equation Markov process Diffusion Itô diffusion Jump diffusion Sample-continuous process "9. Diffusion processes"...

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important...

In mathematics, Itô's lemma or Itô's formula (also called the Itô–Döblin formula) is an identity used in Itô calculus to find the differential of a time-dependent...

Brownian web Geometric Brownian motion – Continuous stochastic process Itô diffusion – Solution to a specific type of stochastic differential equation Lévy...

which can be very expensive. The probability path in diffusions model is defined through an Itô process and one can retrieve the deterministic process...

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of...

{\displaystyle X} be the R n {\displaystyle \mathbf {R} ^{n}} -valued Itô diffusion solving the stochastic differential equation d X t = b ( X t ) d t +...

is a stochastic integral, the most common alternative to the Itô integral. Although the Itô integral is the usual choice in applied mathematics, the Stratonovich...

diffusion Effusion of a gas through small holes Gaseous diffusion Itō diffusion Knudsen diffusion of particles from very small containers Osmosis, the movement...

Hawkes process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process...

stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the most useful...

t)} . The expectation formula above is also valid for N-dimensional Itô diffusions. The corresponding partial differential equation for u : R N × [ 0 ...

The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian...

estimate for the probability that a (scaled-down) sample path of an Itō diffusion will stray far from the mean path. This statement is made precise using...

identically distributed samples. We consider the overdamped Langevin Itô diffusion X ˙ = ∇ log ⁡ π ( X ) + 2 W ˙ {\displaystyle {\dot {X}}=\nabla \log...

that subset of the boundary. More generally, harmonic measure of an Itō diffusion X describes the distribution of X as it hits the boundary of D. In the...

mathematical definition was first proposed by Kiyosi Itô in the 1940s, leading to what is known today as the Itô calculus. Another construction was later proposed...

Hawkes process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process...

com/abstract=1505073. Bertram, W.K., 2009, Optimal Trading Strategies for Ito Diffusion Processes, Physica A, Forthcoming. Available at SSRN: https://ssrn...

Hawkes process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process...

coefficient functions in the SDEs. Consider the Itō diffusion X {\displaystyle X} satisfying the following Itō stochastic differential equation d X t = a (...

field. Let X : [0, +∞) × Ω → Rd be an Itō diffusion defined on a probability space (Ω, Σ, P) and solving the Itō stochastic differential equation d X t...

on several core assumptions that extend the classical framework of Itô diffusion models to accommodate more complex market behavior. These include: The...

generating set in the strict sense. In stochastic analysis, an Itō diffusion or more general Itō process has an infinitesimal generator. The generator of any...

hypothesis, depends continuously upon x. Every Itô diffusion with Lipschitz-continuous drift and diffusion coefficients is a Feller-continuous process....

continuity is the appropriate notion of continuity for processes such as Itō diffusions. X is said to be a Feller-continuous process if, for any fixed t ∈ T...

solution to the Stratonovich SDE is a solution to the Itô SDE. The zero-drift equation with constant diffusion can be considered as a model of classical Brownian...

255–260. doi:10.1090/S0273-0979-1985-15367-4. ISSN 0273-0979. with Kiyosi Itô: Diffusion processes and their sample paths. Springer 1965. Stochastic Integrals...