8 papers
Markov property for systems driven by the Brownian sheet
Nacira Agram, Bernt Øksendal, Frank Proske +1
We study stochastic systems driven by a Brownian sheet and formulate a Markov property adapted to their two-parameter structure. For time-space homogeneous Itô sheets, the future e…
Optimal Stopping for Systems Driven by the Brownian Sheet
Nacira Agram, Bernt Oksendal, Frank Proske +1
We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part we derive explicit solutions to two opt…
SPDE Games Driven by a Brownian Sheet with Applications to Pollution Minimization
Nacira Agram, Bernt Øksendal, Frank Proske +1
This paper studies a nonzero-sum stochastic differential game in the context of shared spatial-domain pollution control. The pollution dynamics are governed by a stochastic partial…
Fokker-Planck equations for conditional McKean-Vlasov systems driven by Brownian sheets
Nacira Agram, Bernt Øksendal, Frank Proske +1
We investigate conditional McKean-Vlasov equations driven by time-space white noise, motivated by the propagation of chaos in an N-particle system with space-time Ornstein-Uhlenbec…
A Kalman filter for linear systems driven by time-space Brownian sheet
Nacira Agram, Bernt Øksendal, Frank Proske +1
We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian…
Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet
Nacira Agram, Bernt Oksendal, Frank Proske +1
In this paper, we consider a McKean-Vlasov (mean-field) stochastic partial differential equations (SPDEs) driven by a Brownian sheet. We study the propagation of chaos for a space-…
Long-time behaviors of some stochastic differential equations driven by Lévy noise
I. Orlovskyi, F. Proske, O. Tymoshenko
Using key tools such as Itô formula for general semi-martingales, moments estimates for Lévy-type stochastic integrals and properties of regular varying functions we find condition…
Optimal control of SPDEs driven by time-space Brownian motion
Nacira Agram, Bernt Øksendal, Frank Proske +1
In this paper we study a Pontryagin type stochastic maximum principle for the optimal control of a system, where the state dynamics satisfy a stochastic partial differential equati…