Hitting properties of parabolic s.p.d.e.’s with reflection
By Robert C. Dalang, Carl Mueller, L. Zambotti. 2004
69 citations recorded by the source corpus.
We study the hitting properties of the solutions u of a class of parabolic stochastic partial differential equations with singular drifts that prevent u from becoming negative. The drifts can be a reflecting term or a nonlinearity cu -3 , with c > 0. We prove that almost surely, for all time t > 0, the solution u t hits the level 0 only at a finite number of space points, which depends explicitly on c. In particular, this number of hits never exceeds 4 and if c > 15/8, then level 0 is not hit.
Subfields: Applied Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/0d60738f3c95e1b7388e78549581880ad39675db
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In Applied Mathematics
- Arnaud Debussche
- L. Zambotti
- Martina Hofmanov'a
- Martin Hairer
- Franco Flandoli
- Panagiotis E. Souganidis
- Benjamin Gess
In Control and Systems Engineering
In Finance
- Arnaud Debussche
- L. Zambotti
- Martina Hofmanov'a
- Martin Hairer
- Panagiotis E. Souganidis
- Benjamin Gess
- Franco Flandoli
- Charles-Edouard Br'ehier
Citations in the corpus
- Conservative stochastic Cahn–Hilliard equation with reflection (2006, background): “3) has been introduced by Nualart and Pardoux in [21] and studied in detail recently: besides existence and uniqueness of solutions, a rather detailed study of the contact set {(t, θ) :vt(θ) = 0} and of the reflection measure ζ has been obtained; see [7, 24, 25].”