Dear all,

Join us for our upcoming talk in the STAR seminar series on Wednesday, February 11th, from 11:00 to 12:00 (Oslo time). 

As always, the talk will take place in a hybrid format: participants in Oslo can attend the talk in Room 723 in Niels Henrik Abels hus, whereas the international audience will be able to follow the talk via Zoom.

The speaker is Rahma Yasmina Moulay Hachemi (University of Saida Dr. Moulay Tahar) with the talk:

Title: The time-fractional stochastic heat equation driven by time-space white noise

Abstract: We study the stochastic time-fractional stochastic heat equation:

∂α/∂tα Y(t, x) = λΔY (t, x) + σ W(t, x); (t, x) ∈ (0,∞) × Rd , (0.1), where d ∈ N = {1, 2, ...} and ∂α/∂tα is the Caputo derivative of order α ∈ (0, 2), and λ > 0 and σ ∈ R are given constants.

We consider the equation in the sense of distribution, and we find an explicit expression for the S-valued solution Y (t, x), where S is the space of tempered distributions.

Following the terminology of Y. Hu [1], we say that the solution is mild if Y (t, x) ∈ L2(P) for all t, x. It is well-known that in the classical case with α = 1, the solution is mild if and only if the space dimension d = 1. We prove that if α ∈ (1, 2) the solution is mild if d = 1 or d = 2. If α < 1 we prove that the solution is not mild for any d.

[1] Hu, Yaozhong (2019): Some recent progress on stochastic heat equations. Acta Mathematica Scientia 39B(3); 874-914

We are looking forward to seeing you!

Best regards,

Giulia, Leonardo, Pere, and David