## Seminars

## Seminars

## Special Probability Seminar——Stochastic calculus aspects of the Vertex Reinforced Jump process

**Holder：** Christophe Sabot(Université Lyon 1)

**Time：**2024-03-25 13:15-14:15

**Location：** Lecture Hall,2nd floor, Building A, Band C, MathematicsCenter

**Abstract: **
In this talk we will present some relations between classical computations on exponential functionals of the Brownian motion and some representation of the Vertex Reinforced Jump Process (VRJP). In particular we will show how the Lamperti transformation, the Markov property of the Matsumoto-Yor process have natural generalizations to the multidimensionnal setting involving the representation of the VRJP by a random Schrödinger operator. Besides, a discrete version of the Matsumoto-Yor porperties appears also, in a rather different way, in terms of some natural functionals associated with the one-dimensional VRJP.

**About the Speaker: **

Christophe Sabot is Professor at Université Lyon 1, and head of the team "Probability, Statistics and Mathematical Physics" of the Institut Camille Jordan. He is specialist of Probability, more specifically he works on interacting random walks: random walks that interact with their past trajectory or with a random environment.

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