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- Title
Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application.
- Authors
Bouaziz, Tayeb; Chala, Adel
- Abstract
We consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1) {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.
- Subjects
WIENER processes; MALLIAVIN calculus; MAXIMUM principles (Mathematics); BROWNIAN motion; FRACTIONAL calculus; FRANKFURTER sausages; MOTION; STOCHASTIC control theory
- Publication
Random Operators & Stochastic Equations, 2020, Vol 28, Issue 4, p291
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/rose-2020-2047