Chuỗi seminar thường kì Khoa Toán Kinh tế được tiếp tục.
Người trình bày: TS. Phạm Công Dân – Data Analyst – Viettel High Tech (Ph.D in Probability and Statistics from Aix-Marseille University)
Chủ đề: The infinite differentiability and monotonicity of the speed for excited random walks
In this presentation, using renewal times and Girsanov’s transform, we prove that the speed of the excited random walk is infinitely differentiable with respect to the bias parameter in (0,1) in dimension d≥2. At the critical point 0, using a special method, we also prove that the speed is differentiable and the derivative is positive for every dimension 2≤d≠3. However, this is not enough to imply that the speed is increasing in a neighborhood of 0. It still remains to prove that the derivative is continuous at 0.
We also introduce a method for studying monotonicity of the speed of excited random walks in high dimensions, based on a formula for the speed obtained via cut-times and Girsanov’s transform. While the method gives rise to similar results as have been or can be obtained via the expansion method of van der Hofstad and Holmes, it may be more palatable to a general probabilistic audience.
