arXiv subjects

Victor Rohde

Publications and source records attributed to Victor Rohde.

6 recordsLinked to original sources

arXiv2020

On non-negative solutions of SDDEs with an application to CARMA processes

This note provides a simple sufficient condition ensuring that solutions of stochastic delay differential equations (SDDEs) driven by subordinators are non-negative. While, to the best of our knowledge, no simple non-negativity conditions are available in the context of SDDEs, we compare our result to the literature within the subclass of invertible continuous-time ARMA (CARMA) processes. In particular, we analyze why our condition cannot be necessary for CARMA($p,q$) processes when $p=2$, and we show that there are various situations where our condition applies while existing results do not as soon as $p\geq 3$. Finally, we extend the result to a multidimensional setting.

math.PR↗

arXiv2020

A surrogate model for estimating extreme tower loads on wind turbines based on random forest proximities

In the present paper we present a surrogate model, which can be used to estimate extreme tower loads on a wind turbine from a number of signals and a suitable simulation tool. Due to the requirements of the International Electrotechnical Commission (IEC) Standard 61400-1, assessing extreme tower loads on wind turbines constitutes a key component of the design phase. The proposed model imputes tower loads by matching observed signals with simulated quantities using proximities induced by random forests. In this way the algorithm's adaptability to high-dimensional and sparse settings is exploited without using regression-based surrogate loads (which may display misleading probabilistic characteristics). Finally, the model is applied to estimate tower loads on an operating wind turbine from data on its operational statistics.

stat.AP↗

arXiv2018

Continuous-time models with an autoregressive structure

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general stochastic delay differential equations, will be given particular attention. We use the obtained results to link the introduced processes to both discrete-time and continuous-time ARMA processes.

math.PR↗

arXiv2018

Stochastic differential equations with a fractionally filtered delay: a semimartingale model for long-range dependent processes

In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying autocovariance functions. The model departs from the usual way of incorporating this type of long-range dependence into a short-memory model as it is obtained by applying a fractional filter to the drift term rather than to the noise term. The advantages of this approach are that the corresponding long-range dependent solutions are semimartingales and the local behavior of the sample paths is unaffected by the degree of long memory. We prove existence and uniqueness of solutions to the SFDDEs and study their spectral densities and autocovariance functions. Moreover, we define a subclass of SFDDEs which we study in detail and relate to the well-known fractionally integrated CARMA processes. Finally, we consider the task of simulating from the defining SFDDEs.

math.PR↗

arXiv2018

Multivariate stochastic delay differential equations and CAR representations of CARMA processes

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a continuous-time equivalent of the AR($\infty$) representation. Furthermore, we show how this representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.

math.PR↗

arXiv2017

On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos

Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient conditions. The case where both components consist of a sum of two Gaussian squares is treated in more depth, and it is conjectured that such vectors are infinitely divisible.

math.PR↗