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E. Hausenblas

Publications and source records attributed to E. Hausenblas.

2 recordsLinked to original sources
arXiv2017

Existence of a density of the 2Dim Stochastic Navier Stokes Equation driven by Levy processes or fractional Brownian motion

In this article we are interested in the regularity properties of the probability measure induced by the solution process of the Lévy noise or a fractional Brownian motion driven Navier Stokes Equation on the two dimensional torus $\mathbb{T}$. We mainly investigate under which conditions on the characteristic measure of the Lévy process or the Hurst parameter of the fractal Brownian motion the law of the projection of $u(t)$ onto any finite dimensional $F\subset L^2(\mathbb{T})$ is absolutely continuous with respect to the Lebesgue measure on $F$.

math.PR↗
arXiv2017

Nonlinear filtering with correlated Lévy noise characterized by copulas

The objective in stochastic filtering is to reconstruct information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy transformation of that process. Usually X and Y are modeled by stochastic differential equations driven by a Brownian motion or a jump (or Levy) process. We are interested in the situation where both the state process X and the observation process Y are perturbed by coupled Levy processes. More precisely, L=(L_1,L_2) is a 2--dimensional Levy process in which the structure of dependence is described by a Levy copula. We derive the associated Zakai equation for the density process and establish sufficient conditions depending on the copula and $L$ for the solvability of the corresponding solution to the Zakai equation. In particular, we give conditions of existence and uniqueness of the density process, if one is interested to estimate quantities like P( X(t)>a), where a is a threshold.

math.PR↗