On the representation of solutions of anticipating
Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 38-47
Cet article a éte moissonné depuis la source Math-Net.Ru
The unique solution of an anticipating linear partial stochastic differential equation is constructed by means of the Fourier transformation.
Keywords:
Anticipating initial condition, extended stochastic integral, partial stochastic differential equation.
@article{THSP_2007_13_3_a4,
author = {Alexandr V. Ilchenko},
title = {On the representation of solutions of anticipating},
journal = {Teori\^a slu\v{c}ajnyh processov},
pages = {38--47},
year = {2007},
volume = {13},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a4/}
}
Alexandr V. Ilchenko. On the representation of solutions of anticipating. Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 38-47. http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a4/
[1] A. A. Dorogovtsev, “Anticipating equations and fltration problem”, Theory of Stochastic Processes, 3(19):1–2 (1997), 154–163
[2] A. A. Dorogovtsev, Stochastic Analysis and Random Maps in Hilbert Space, VSP, Utrecht, 1994
[3] A. A. Dorogovtsev, “One formula for the solution of Itô–Volterra equation with the extended stochastic integral”, Random Processes and Infinitely Dimensional Analysis, Inst. Math., Kyiv, 1992, 41–56 (Russian)
[4] L. Hörmander, The Analysis of Linear Partial Differential Operators, v. 1, Springer, Berlin, 1983
[5] D. Nualart, The Malliavin Calculus and Related Topics, Springer, Berlin, 1995
[6] A. V. Skorokhod, “One generalization of the stochastic integral”, Probability Theory and Applications, 20:2 (1975), 223–237