5 citations · 9 across the 6 of their papers we have counts for
7 papers · 1 filter
On non-negative solutions of SDDEs with an application to CARMA processes
Mikkel Slot Nielsen, Victor Rohde
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…
On non-stationary solutions to MSDDEs: representations and the cointegration space
Mikkel Slot Nielsen
In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) which have stationary increments, and we show that this modeling framework is in m…
Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages
Mikkel Slot Nielsen, Jan Pedersen
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estima…
Stochastic differential equations with a fractionally filtered delay: a semimartingale model for long-range dependent processes
Richard A. Davis, Mikkel Slot Nielsen, Victor Rohde
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…
Multivariate stochastic delay differential equations and CAR representations of CARMA processes
Andreas Basse-O'Connor, Mikkel Slot Nielsen, Jan Pedersen +1
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…
Equivalent martingale measures for Lévy-driven moving averages and related processes
Andreas Basse-O'Connor, Mikkel Slot Nielsen, Jan Pedersen
In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for Lévy-driven moving averages and other non-Markovian jump processes. The…
Continuous-time models with an autoregressive structure
Andreas Basse-O'Connor, Mikkel Slot Nielsen, Jan Pedersen +1
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 pr…