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This paper provides a brief overview of the stochastic modeling of variance swap curves. Focus is on affine factor models. We propose a novel drift parametrization which assures that the components of the state process can be matched with any pre-specified ...
We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...
In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system ...
The subject of the present thesis is an optimal prediction problem concerning the ultimate maximum of a stable Lévy process over a finite interval of time. Such "optimal prediction" problems are of both theoretical and practical interest, in particular the ...
Within systems biology there is an increasing interest in the stochastic behavior of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous-time Markov chain (CTMC). S ...
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Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxi ...
We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk [5]. We recapture and make use of the convenient calculus on Frechet spaces, as ...
This work focuses on the stochastic properties of boresight determination between a strapdown IMU and a frame-based imaging sensor. The core of the stochastic model is a rigorous error propagation of the estimated input accuracies and their correlations. ...
We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...
A continuous time process of alternating stochastic growths and deterministic decays is proposed as a simple model for the interannual dynamics of snow water equivalent (SWE) storage and melting. The related stationary properties are studied, and an integr ...
