Introduction to the Theory of the It$\hat{o}$-type Stochastic Integrals and Stochastic Differential Equations
Zbornik radova, Tome 8 (1998) no. 16, p. 105
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
The theory of stochastic differential equations, as a part of the general theory
of stochastic processe:;, began to develop in the fifties in the discussions of U.
Gikhman, and independently of him, K. Ita. The accepted terminology, however,
derived from Ita. In his papers [15], [16], [17], for special classes of stochastic
processes he introduced the notion of the stochastic integral and of the stochastic
differential equation with respect to a Wiener process. Following the classical
theory of ordinary differential equations, he proved the fundamental theorem of
the existence and uniqueness of solutions and also the Markov property of solutions.
From then on this theory has developed in several aspects, mostly induced
by mathematical abstractions or by many applications in technical practice, having
in mind that a Gaussian white noise could be mathematically interpreted by a
Wiener process.
@article{ZR_1998_8_16_a3,
author = {Svetlana Jankovi\'c},
title = {Introduction to the {Theory} of the {It}$\hat{o}$-type {Stochastic} {Integrals} and {Stochastic} {Differential} {Equations}},
journal = {Zbornik radova},
pages = {105 },
year = {1998},
volume = {8},
number = {16},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZR_1998_8_16_a3/}
}
Svetlana Janković. Introduction to the Theory of the It$\hat{o}$-type Stochastic Integrals and Stochastic Differential Equations. Zbornik radova, Tome 8 (1998) no. 16, p. 105 . http://geodesic.mathdoc.fr/item/ZR_1998_8_16_a3/