Bessel SPDEs with general Dirichlet boundary conditions
Copyright policy )Bessel SPDEs with general Dirichlet boundary conditions
We generalise the integration by parts formulae obtained in arXiv:1811.00518v5 [math.PR] to Bessel bridges on $[0,1]$ with arbitrary boundary values, as well as Bessel processes with arbitrary initial conditions. This allows us to write, formally, the corresponding dynamics using renormalised local times, thus extending the Bessel SPDEs of arXiv:1811.00518v5 [math.PR] to general Dirichlet boundary conditions. We also prove a dynamical result for the case of dimension $2$, by providing a weak construction of the gradient dynamics corresponding to a $2$-dimensional Bessel bridge.
41 pages
- UNIVERSITE PARIS DESCARTES France
- Sorbonne University France
- Sorbonne Paris Cité France
- Imperial College London United Kingdom
- French National Centre for Scientific Research France
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Dirichlet forms, Probability (math.PR), [MATH] Mathematics [math], integration by parts formulae, local times, Bessel processes, singular SPDEs, Stochastic partial differential equations (aspects of stochastic analysis), renormalisation, Singular stochastic partial differential equations, FOS: Mathematics, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Dirichlet forms, Probability (math.PR), [MATH] Mathematics [math], integration by parts formulae, local times, Bessel processes, singular SPDEs, Stochastic partial differential equations (aspects of stochastic analysis), renormalisation, Singular stochastic partial differential equations, FOS: Mathematics, Mathematics - Probability
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