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- Xuerong Mao, Markus Riedle
- Systems & Control Letters
- 2006

The mean square stability of a non-linear stochastic Volterra integro-differential equation is studied. Non-convolution Volterra terms arise in both the drift and the dispersion term. Moreover, forâ€¦ (More)

Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notionsâ€¦ (More)

A generalization of Ã‰meryâ€™s inequality for stochastic integrals is shown for convolution integrals of the form ( âˆ« t 0 g(t âˆ’ s)Y (sâˆ’) dZ(s))t>0, where Z is a semimartingale, Y an adapted cÃ dlÃ gâ€¦ (More)

A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued LÃ©vy processes is defined. There are no conditions on the Banach spaces nor on the LÃ©vyâ€¦ (More)

- Markus Riedle
- 2008

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definitionâ€¦ (More)

- Xuerong Mao, Markus Riedle
- 2007

A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficients depend linearly on the past of the solution, i.e. a linearâ€¦ (More)

- John A. D. Appleby, Markus Riedle, Catherine Swords
- Finance and Stochastics
- 2013

This paper studies the asymptotic behaviour of an affine stochastic functional differential equation modelling the evolution of the cumulative return of a risky security. In the model, the traders ofâ€¦ (More)

- Markus Riedle
- 2014

In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical LÃ©vy processes in separable Banach spaces. Here, a cylindrical LÃ©vyâ€¦ (More)

- Markus Riedle
- 2005

In this article we consider solutions of affine stochastic functional differential equations on R. The drift of these equations is specified by a functional defined on a general function space Bâ€¦ (More)

- Markus Riedle
- 2007

In the following paper, we provide a stochastic analogue to work of Shea and Wainger by showing that when the measure and state-independent diffusion coefficient of a linear ItÃ´â€“Volterra equation areâ€¦ (More)