TY  - JOUR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
T1  - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications
JF  - Stochastic processes and their application
N2  - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
KW  - Stochastic differential equations
KW  - Multiplicative Levy noise
KW  - Levy type processes
KW  - Heavy-tailed distributions
KW  - Model selection
KW  - Wasserstein distance
KW  - Time series
Y1  - 2017
U6  - https://doi.org/10.1016/j.spa.2017.09.003
SN  - 0304-4149
SN  - 1879-209X
VL  - 128
IS  - 7
SP  - 2153
EP  - 2178
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Synodinos, Alexis D.
A1  - Tietjen, Britta
A1  - Lohmann, Dirk
A1  - Jeltsch, Florian
T1  - The impact of inter-annual rainfall variability on African savannas changes with mean rainfall
JF  - Journal of theoretical biology
N2  - Savannas are mixed tree-grass ecosystems whose dynamics are predominantly regulated by resource competition and the temporal variability in climatic and environmental factors such as rainfall and fire. Hence, increasing inter-annual rainfall variability due to climate change could have a significant impact on savannas. To investigate this, we used an ecohydrological model of stochastic differential equations and simulated African savanna dynamics along a gradient of mean annual rainfall (520–780 mm/year) for a range of inter-annual rainfall variabilities. Our simulations produced alternative states of grassland and savanna across the mean rainfall gradient. Increasing inter-annual variability had a negative effect on the savanna state under dry conditions (520 mm/year), and a positive effect under moister conditions (580–780 mm/year). The former resulted from the net negative effect of dry and wet extremes on trees. In semi-arid conditions (520 mm/year), dry extremes caused a loss of tree cover, which could not be recovered during wet extremes because of strong resource competition and the increased frequency of fires. At high mean rainfall (780 mm/year), increased variability enhanced savanna resilience. Here, resources were no longer limiting and the slow tree dynamics buffered against variability by maintaining a stable population during ‘dry’ extremes, providing the basis for growth during wet extremes. Simultaneously, high rainfall years had a weak marginal benefit on grass cover due to density-regulation and grazing. Our results suggest that the effects of the slow tree and fast grass dynamics on tree-grass interactions will become a major determinant of the savanna vegetation composition with increasing rainfall variability.
KW  - Rainfall variability
KW  - Savanna-grassland bistability
KW  - Stochastic differential equations
KW  - Coexistence mechanisms
KW  - Fire
Y1  - 2017
U6  - https://doi.org/10.1016/j.jtbi.2017.10.019
SN  - 0022-5193
SN  - 1095-8541
VL  - 437
SP  - 92
EP  - 100
PB  - Elsevier Ltd.
CY  - London
ER  -