A Reflected Stochastic Heat Equation as Symmetric Dynamics with Respect to the 3-d Bessel Bridge
By L. Zambotti. 2001
72 citations recorded by the source corpus.
Abstract We prove that a stochastic heat equation with reflection at 0, on the spatial interval [0, 1] with Dirichlet boundary conditions and additive white-noise, admits an explicit symmetrizing invariant measure on C ([0, 1]): the 3-d Bessel Bridge, i.e., the law of the modulus of a 3-dimensional Brownian motion conditioned to be 0 at time 1, a classical measure in probability theory, also connected with the theory of excursions of Brownian motion. This is a non-trivial example of a Gibbs-type measure being singular with respect to the reference Gaussian measure and concentrated on the convex set of positive, continuous functions on [0, 1].
Subfields: Finance, Mathematical Physics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/e199879f1cf87abb9f8ddb8c6d9fe78842e4c75f
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In Finance
- Tusheng Zhang
- Steven N. Evans
- A. Winter
- L. Zambotti
- Xicheng Zhang
- Peter K. Friz
- Wei Liu
- Nicolas Victoir
In Mathematical Physics
- A. Winter
- Steven N. Evans
- Tusheng Zhang
- Peter Pfaffelhuber
- Andrea Greven
- A. Depperschmidt
- L. Zambotti
- Matthias Winkel
In Modeling and Simulation
Citations in the corpus
- White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities (2010, background): “It was shown in [14] that {Tt, t ≥ 0} forms a Markovian semigroup.”
- Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection (2002, background): “where µ3 is the law on L 2 (0, 1; R 3 ) of a Brownian Bridge of dimension 3 between 0 and 0 over [0, 1], F, G : H 3 � R and ∇F : H 3 � H 3 is the gradient of F in H 3 . It is well known that (( 3 ,W 1,2 (µ3)) generates the process Z3, solution of the R 3 -valued linear SPDE (10): see [ 20 ] and Chap”
- SUBTREE PRUNE AND REGRAFT: A REVERSIBLE REAL TREE-VALUED MARKOV PROCESS (2005, background): “We remark that excursion path-valued Markov processes that are reversible with respect to the distribution of standard Brownian excursion and have continuous sample paths have been investigated in [34, 35, 36], and that these processes can also be thought of as real tree-valued diffusion processes t”
- Tree-valued Fleming–Viot dynamics with mutation and selection (2011, background): “Note that the resulting processes are among the first tree-valued stochastic processes in the literature [but see also Zambotti (2001, 2002, 2003), Evans, Pitman and Winter (2006), Evans and Winter (2006), Evans and Lidman (2007)].”