Zobrazeno 1 - 10
of 441
pro vyhledávání: '"A. Oksendal"'
In this paper, we study the probability distribution of solutions of McKean-Vlasov stochastic differential equations (SDEs) driven by fractional Brownian motion. We prove the associated Fokker-Planck equation, which governs the evolution of the proba
Externí odkaz:
http://arxiv.org/abs/2409.07029
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 sheets. We derive a stochastic integral equation for the conditional v
Externí odkaz:
http://arxiv.org/abs/2407.06386
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, a
Externí odkaz:
http://arxiv.org/abs/2407.13688
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-time Ornstein-Uhlenbeck SPDE type. Subsequently, we prove the existenc
Externí odkaz:
http://arxiv.org/abs/2404.19490
We give an introduction to the time-fractional stochastic heat equation driven by 1+d-parameter fractional time-space white noise, in the following two cases: (i) With additive noise (ii) With multiplicative noise. The fractional time derivative is i
Externí odkaz:
http://arxiv.org/abs/2402.16900
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 equation (SPDE) driven by a two-parameter (time-space) Brownian motion (also
Externí odkaz:
http://arxiv.org/abs/2308.00173
Autor:
Đorđević, Jasmina, Øksendal, Bernt
The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with H>0.5. For this, we summarise the theory of fractional white noise and prove a fundamental L^2-estimate for WIS-integrals. We apply t
Externí odkaz:
http://arxiv.org/abs/2306.08324
Autor:
Agram, Nacira, Øksendal, Bernt
The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean-Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely continuous with re
Externí odkaz:
http://arxiv.org/abs/2302.12522
This paper establishes a verification theorem for impulse control problems involving conditional McKean-Vlasov jump diffusions. We obtain a Markovian system by combining the state equation of the problem with the stochastic Fokker-Planck equation for
Externí odkaz:
http://arxiv.org/abs/2301.01506
We study the time-fractional stochastic heat equation driven by time-space white noise with space dimension $d\in\mathbb{N}=\{1,2,...\}$ and the fractional time-derivative is the Caputo derivative of order $\alpha \in (0,2)$. We consider the equation
Externí odkaz:
http://arxiv.org/abs/2211.12861