arXiv subjects

Frank Proske

Publications and source records attributed to Frank Proske.

39 records · Page 3Linked to original sources

arXiv2013

On the Construction and Malliavin Differentiability of Levy Noise Driven SDEs with Singular Coefficients

In this paper we introduce a new technique to construct unique strong solutions of SDEs with singular coefficients driven by certain Levy processes. Our method which is based on Malliavin calculus does not rely on a pathwise uniqueness argument. Furthermore, the approach, which provides a direct construction principle, grants the additional insight that the obtained solutions are Malliavin differentiable.

math.PR↗

arXiv2012

Maximum principles for jump diffusion processes with infinite horizon

We prove maximum principles for the problem of optimal control for a jump diffusion with infinite horizon and partial information. The results are applied to partial information optimal consumption and portfolio problems in infinite horizon.

math.OC↗

arXiv2004

Stochastic partial differential equations driven by Levy space-time white noise

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d\leq 3, then this solution can be represented as a classical random field in L2(μ), where μis the probability law of the Levy process. The starting point of our theory is a chaos expansion in terms of generalized Charlier polynomials. Based on this expansion we define Kondratiev spaces and the Levy Hermite transform.

math.PR↗