Research-STABLE PROCESS WITH SINGULAR DRIFT

Research

Probability & Statistics Seminar

STABLE PROCESS WITH SINGULAR DRIFT

Speaker: Jin Peng
Time: Sep 6, 2016, 16:10-17:10
Location: Conference Room 706, Service Center of Scientific Research and Teaching

Let d ≥ 2. In this talk, we consider weak solutions for the following type of stochastic diﬀerential equation

X₀ = x, dX_t = dS_t + b(s + t, X_t)dt, t ≥ 0,

where (s, x) ∈ R₊ × R^d is the initial starting point, b : R₊ × R^d → R^d is measurable, and S = (S_t)_t≥₀ is a d-dimensional α-stable process with index α ∈ (1, 2). We show that if the α-stable process S is non-degenerate and

b ∈ L^∞_loc(R₊; L^∞(R^d)) + L^q_loc(R₊; L ^p(R^d))

for some p, q > 0 with d/p + α/q <α − 1, then the above SDE has a unique weak solution for every starting point (s, x) ∈ R₊ × R^d.