TY - ELEC
AU - Mueller, Carl
PY - 2018
TI - Hitting questions and multiple points for stochastic PDE in the critical case
LA - eng
M3 - Moving Image
AB - Hitting questions play a central role in the theory of Markov processes. For
example, it is well known that Brownian motion hits points in one dimension,
but not in higher dimensions. For a general Markov process, we can determine
whether the process hits a given set in terms of potential theory. There has
also been a huge amount of work on the related question of when a process has
multiple points.
For stochastic partial differential equations (SPDE), much less is known, but
there has been a growing number of papers on the topic in recent years.
Potential theory provides an answer in principle. But unfortunately,
solutions to SPDE are infinite dimensional processes, and the potential theory
is intractible. As usual, the critical case is the most difficult.
We will give a brief survey of known results, followed by a discussion of an
ongoing project with R. Dalang, Y. Xiao, and S. Tindel which promises to
answer questions about hitting points and the existence of multiple points in
the critical case.
N2 - Hitting questions play a central role in the theory of Markov processes. For
example, it is well known that Brownian motion hits points in one dimension,
but not in higher dimensions. For a general Markov process, we can determine
whether the process hits a given set in terms of potential theory. There has
also been a huge amount of work on the related question of when a process has
multiple points.
For stochastic partial differential equations (SPDE), much less is known, but
there has been a growing number of papers on the topic in recent years.
Potential theory provides an answer in principle. But unfortunately,
solutions to SPDE are infinite dimensional processes, and the potential theory
is intractible. As usual, the critical case is the most difficult.
We will give a brief survey of known results, followed by a discussion of an
ongoing project with R. Dalang, Y. Xiao, and S. Tindel which promises to
answer questions about hitting points and the existence of multiple points in
the critical case.
UR - https://open.library.ubc.ca/collections/48630/items/1.0377320
ER - End of Reference