23.IV.2024
Alexey Kuznetsov, York University, Toronto, Canada
"Darboux transformation of diffusion processes"
Abstract: Darboux transformation is a well-known technique in the study of second order linear differential operators and it has many applications, for example, in the construction of exactly solvable Shrodinger operators and in the theory of exceptional orthogonal polynomials. In this talk we will define Darboux transform of a killed Brownian motion process and we will explain how it is connected to Siegmund transform and Krein dual strings. We will present several explicit examples of Darboux transformation of Brownian motion (with various boundary conditions) and Ornstein-Uhlenbeck process. This talk is based on joint work with Minjian Yuan.
Alexey Kuznetsov, York University, Toronto, Canada
"Darboux transformation of diffusion processes"
Abstract: Darboux transformation is a well-known technique in the study of second order linear differential operators and it has many applications, for example, in the construction of exactly solvable Shrodinger operators and in the theory of exceptional orthogonal polynomials. In this talk we will define Darboux transform of a killed Brownian motion process and we will explain how it is connected to Siegmund transform and Krein dual strings. We will present several explicit examples of Darboux transformation of Brownian motion (with various boundary conditions) and Ornstein-Uhlenbeck process. This talk is based on joint work with Minjian Yuan.
Everyone is cordially invited!
B. Kołodziejek, W. Matysiak, K. Szpojankowski, J. Wesołowski