Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

Existence and uniqueness of a mild solution to the stochastic heat equation with white and fractional noises


Authors: Yu. Mishura, K. Ralchenko and G. Shevchenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 149-170
MSC (2010): Primary 60H15, 35R60, 35K55, 60G22
DOI: https://doi.org/10.1090/tpms/1068
Published electronically: August 19, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $ D \subset \mathbb{R}^d$ and involving standard and fractional $ L^2(D)$-valued Brownian motions. We assume that the coefficients are homogeneous, Lipschitz continuous, and the coefficient at the fractional Brownian motion is an affine function.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60H15, 35R60, 35K55, 60G22

Retrieve articles in all journals with MSC (2010): 60H15, 35R60, 35K55, 60G22


Additional Information

Yu. Mishura
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska, 01601 Kyiv, Ukraine
Email: myus@univ.kiev.ua

K. Ralchenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska, 01601 Kyiv, Ukraine
Email: k.ralchenko@gmail.com

G. Shevchenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska, 01601 Kyiv, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1068
Keywords: Fractional Brownian motion, stochastic partial differential equation, Green's function
Received by editor(s): March 5, 2018
Published electronically: August 19, 2019
Article copyright: © Copyright 2019 American Mathematical Society