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...

Itô's theorem is a result in the mathematical discipline of representation theory due to Noboru Itô. It generalizes the well-known result that the dimension...

the interval is used. Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula...

The Itô–Nisio theorem is a theorem from probability theory that characterizes convergence in Banach spaces. The theorem shows the equivalence of the different...

In particular, the Itô's lemma's best known application is in the derivation of the Black–Scholes equation for option values. Itô's methods are also used...

representation Glossary of representation theory Group representation Itô's theorem List of representation theory topics List of harmonic analysis topics...

(any of several named after Carl Friedrich Gauss) Greendlinger's lemma Itô's lemma Jordan's lemma Lovász local lemma Nakayama's lemma Poincaré's lemma...

the Marcus integral, and the Ogawa integral. Mathematics portal Itô calculus Itô's lemma Stratonovich integral Semimartingale Wiener process Thomas Mikosch...

Goodstein's theorem Green's theorem (to do) Green's theorem when D is a simple region Heine–Borel theorem Intermediate value theorem Itô's lemma Kőnig's...

deviations of Gaussian random functions Girsanov's theorem Hawkes process Increasing process Itô's lemma Jump diffusion Law of the iterated logarithm...

Brownian motion can be written in terms of an Itô integral with respect to this Brownian motion. The theorem only asserts the existence of the representation...

In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity...

speaking, the Freidlin–Wentzell theorem gives an estimate for the probability that a (scaled-down) sample path of an Itō diffusion will stray far from the...

uniqueness in distribution. In its original form, the theorem was stated for n {\displaystyle n} -dimensional Itô equations and was proven by Toshio Yamada and...

§ Quantitative finance Fourier transform Girsanov theorem Itô's lemma Martingale representation theorem Mathematical models Mathematical optimization Linear...

{\displaystyle f\in C^{2,1}(\mathbb {R} ^{d}\times [\tau ,\infty ))} , apply Itô's formula: d f ( X t , t ) = ( ∂ f ∂ t + ∑ i = 1 d b i ∂ f ∂ x i + v ∑ i ...

decomposition theorem provides a way to decompose a measure into two distinct parts based on their relationship with another measure. The theorem states that...

In mathematics, the Clark–Ocone theorem (also known as the Clark–Ocone–Haussmann theorem or formula) is a theorem of stochastic analysis. It expresses...

made precise using rate functions. Schilder's theorem is generalized by the Freidlin–Wentzell theorem for Itō diffusions. Let C0 = C0([0, T]; Rd) be the...

least squares Itô calculus Itô isometry Itô's lemma Jaccard index Jackknife (statistics) Jackson network Jackson's theorem (queueing theory) Jadad scale...

uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions...

decimation Cohen et al. 1982 Hall 2015 Theorem 2.11 Trotter 1959 Kato 1978 Hall 2013 Theorem 20.1 Appelbaum 2019 Ito & Kappel 1998 Albeverio, Sergio A.;...

{\displaystyle X_{t}} is also a Gaussian process. In other cases, the central limit theorem indicates that X t {\displaystyle X_{t}} will be approximately normally...

equation with the pure diffusion Monte Carlo method. Itô's lemma Kunita–Watanabe inequality Girsanov theorem Kolmogorov backward equation Kolmogorov forward...

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

does; instead one has to use the slightly more complicated Itô's lemma. Conversion between Itô and Stratonovich integrals may be performed using the formula...

Infinitesimal generator Itô integral Itô's lemma Karhunen–Loève theorem Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric...

and Shinzo Watanabe and plays a fundamental role in their extension of Ito's stochastic integral to square-integrable martingales. Let M, N be continuous...

Girsanov theorem Green measure Heston model / fnc Hörmander's condition / anl Infinitesimal generator Itô's lemma Itô calculus Itô diffusion Itô isometry...

{\displaystyle \mathrm {d} X_{t}^{j}} " can be defined in the sense of Itô. However, Itô's calculus is defined in the sense of L 2 {\displaystyle L^{2}} and...