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pro vyhledávání: '"Schickentanz, Dominic T."'
We condition a Brownian motion on having an atypically small $L_2$-norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2312.12982
We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion. Moreover, we e
Externí odkaz:
http://arxiv.org/abs/2308.04866
We condition a Brownian motion with arbitrary starting point $y \in \mathbb{R}$ on spending at most $1$ time unit below $0$ and provide an explicit description of the resulting process. In particular, we provide explicit formulas for the distribution
Externí odkaz:
http://arxiv.org/abs/2104.06354
Publikováno v:
In Stochastic Processes and their Applications April 2022 146:360-381
