Electronic Communications in Probability

On stochastic heat equation with measure initial data

Jingyu Huang

Full-text: Open access

Abstract

The aim of this short note is to obtain the existence, uniqueness and moment upper bounds of the solution to a stochastic heat equation with measure initial data, without using the iteration method in [1, 2, 3].

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 40, 6 pp.

Dates
Received: 14 December 2016
Accepted: 26 June 2017
First available in Project Euclid: 11 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1502416901

Digital Object Identifier
doi:10.1214/17-ECP71

Mathematical Reviews number (MathSciNet)
MR3685238

Zentralblatt MATH identifier
1379.60070

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60G60: Random fields

Keywords
stochastic heat equation measure initial data Lévy bridge

Rights
Creative Commons Attribution 4.0 International License.

Citation

Huang, Jingyu. On stochastic heat equation with measure initial data. Electron. Commun. Probab. 22 (2017), paper no. 40, 6 pp. doi:10.1214/17-ECP71. https://projecteuclid.org/euclid.ecp/1502416901


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References

  • [1] Le Chen and Robert Dalang: Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions. Annals of Probability, Vol. 43, No. 6, 3006–3051, 2015.
  • [2] Le Chen and Robert Dalang: Moments, intermittency and growth indices for the nonlinear fractional stochastic heat equation. Stoch. Partial Differ. Equ. Anal. Comput. 3 (2015), no. 3, 360–397.
  • [3] Le Chen and Kunwoo Kim: Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency. arXiv preprint https://arxiv.org/abs/1510.06046.
  • [4] Burgess Davis: On the $L^p$ norms of stochastic integrals and other martingales. Duke Math. J. 43 (1976), no. 4, 697–704.
  • [5] Mohammud Foondun and Davar Khoshnevisan: On the stochastic heat equation with spatially-colored random forcing. Trans. Amer. Math. Soc. 365 (2013), no. 1, 409–458.
  • [6] John Walsh: An Introduction to Stochastic Partial Differential Equations. École d’été de probabilités de Saint-Flour XIV (1984) 265-439. In: Lecture Notes in Math. 1180 Springer, Berlin.