Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations. [PDF]
PLoS One, 2018 We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding.
Vet S +5 more
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Food Web Assembly Rules for Generalized Lotka-Volterra Equations. [PDF]
PLoS Comput Biol, 2016 In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the
Haerter JO, Mitarai N, Sneppen K.
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Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria. [PDF]
Physical Review Letters, 2022 We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method.
V. Ros +4 more
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On the existence of weak solutions to stochastic Volterra equations [PDF]
Electronic Communications in Probability, 2022 The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented approach is based on
David J. Promel, David Scheffels
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Approximation of Stochastic Volterra Equations with kernels of completely monotone type [PDF]
Mathematics of Computation, 2021 In this work, we develop a multifactor approximation for $d$-dimensional Stochastic Volterra Equations (SVE) with Lipschitz coefficients and kernels of completely monotone type that may be singular.
A. Alfonsi, Ahmed Kebaier
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Markovian approximations of stochastic Volterra equations with the fractional kernel [PDF]
Quantitative finance (Print), 2021 We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model.
Christian Bayer, Simon Breneis
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Linear-quadratic control for a class of stochastic Volterra equations: Solvability and approximation [PDF]
The Annals of Applied Probability, 2019 We provide an exhaustive treatment of Linear-Quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite.
Eduardo Abi Jaber, Enzo Miller, H. Pham
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Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels [PDF]
Bernoulli, 2019 We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in ...
Eduardo Abi Jaber
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A weak solution theory for stochastic Volterra equations of convolution type [PDF]
The Annals of Applied Probability, 2019 We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels.
Eduardo Abi Jaber +3 more
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A Dynamic Analysis of Energy Storage With Renewable and Diesel Generation Using Volterra Equations [PDF]
IEEE Transactions on Industrial Informatics, 2019 Energy storage systems will play a key role in the power system of the 21st century considering the large penetrations of variable renewable energy, growth in transport electrification, and decentralization of heating loads. Therefore, reliable real-time
D. N. Sidorov +7 more
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