82 citations · 154 across the 37 of their papers we have counts for
43 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…
On the Analysis of a Singular Stochastic Volterra Differential Equation driven by a Wiener Noise
Emmanuel Coffie, Olivier Menoukeu-Pamen, Frank Proske
In this article, we construct unique strong solutions to a class of stochastic Volterra differential equations driven by a singular drift vector field and a Wiener noise. Further,…
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…
Strong solutions of fractional Brownian sheet driven SDEs with integrable drift
Antoine-Marie Bogso, Olivier Menoukeu Pamen, Frank Proske
We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fra…
An SDE for Modeling SAM: Theory and Insights
Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto +3
We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic…
Smoothness of solutions of hyperbolic stochastic partial differential equations with -vector fields
Antoine-Marie Bogso, Moustapha Dieye, Olivier Menoukeu Pamen +1
In this paper we are interested in a quasi-linear hyperbolic stochastic differential equation (HSPDE) when the vector field is merely bounded and measurable. Although the determini…
On the Theoretical Properties of Noise Correlation in Stochastic Optimization
Aurelien Lucchi, Frank Proske, Antonio Orvieto +2
Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that…
Mean first exit times of Ornstein-Uhlenbeck processes in high-dimensional spaces
Hans Kersting, Antonio Orvieto, Frank Proske +1
The -dimensional Ornstein--Uhlenbeck process (OUP) describes the trajectory of a particle in a -dimensional, spherically symmetric, quadratic potential. The OUP is composed o…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Li…
On the Analysis of a Generalised Rough Ait-Sahalia Interest Rate Model
Emmanuel Coffie, Xuerong Mao, Frank Proske
Fractional Brownian motion with the Hurst parameter is used widely, for instance, to describe a 'rough' stochastic volatility process in finance. In this paper, we…
Anticorrelated Noise Injection for Improved Generalization
Antonio Orvieto, Hans Kersting, Frank Proske +2
Injecting artificial noise into gradient descent (GD) is commonly employed to improve the performance of machine learning models. Usually, uncorrelated noise is used in such pertur…
Sensitivity Analysis with respect to a Stock Price Model with Rough Volatility via a Bismut-Elworthy-Li Formula for Singular SDEs
Emmanuel Coffie, Sindre Duedahl, Frank Proske
In this paper, we show the existence of unique Malliavin differentiable solutions to SDE`s driven by a fractional Brownian motion with Hurst parameter H<1/2 and singular, unbounded…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic c…
Takagi type functions and dynamical systems: the smoothness of the SBR measure and the existence and smoothness of local time
P. Imkeller, O. Menoukeu Pamen, F. Proske
We investigate the occupation measures and local times of Takagi-type functions with roughness parameter , which are Hölder continuous with exponent …
Small Noise Perturbations in Multidimensional Case
Andrey Pilipenko, Frank Norbert Proske
In this paper we study zero-noise limits of stable noise perturbed ODE's which are driven by an irregular vector field with asymptotics $% A(x)\sim \overline{a}(\frac{x}{\l…
Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space
Emmanuel Coffie, Sindre Duedahl, Frank Proske
In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the stat…
Well-posedness of the Deterministic Transport Equation with Singular Velocity Field Perturbed along Fractional Brownian Paths
Oussama Amine, Abdol-Reza Mansouri, Frank Proske
In this article we prove path-by-path uniqueness in the sense of Davie \cite{Davie07} and Shaposhnikov \cite{Shaposhnikov16} for SDE's driven by a fractional Brownian motion with a…
Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise
David Baños, Martin Bauer, Thilo Meyer-Brandis +1
In this paper we aim at generalizing the results of A. K. Zvonkin and A. Y. Veretennikov on the construction of unique strong solutions of stochastic differential equations with si…