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arXiv · 1812.09675

On a class of stochastic differential equations with random and Hölder continuous coefficients arising in biological modeling

Enrico Bernardi·Vinayak Chuni·Alberto Lanconelli
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Abstract

Inspired by the paper Greenhalgh et al. [5] we investigate a class of two dimensional stochastic differential equations related to susceptible-infected-susceptible epidemic models with demographic stochasticity. While preserving the key features of the model considered in [5], where an ad hoc approach has been utilized to prove existence, uniqueness and non explosivity of the solution, we consider an encompassing family of models described by a stochastic differential equation with random and Hölder continuous coefficients. We prove the existence of a unique strong solution by means of a Cauchy-Euler-Peano approximation scheme which is shown to converge in the proper topologies to the unique solution

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Enrico Bernardi, Vinayak Chuni, Alberto Lanconelli. 2018-12-23. On a class of stochastic differential equations with random and Hölder continuous coefficients arising in biological modeling. https://doi.org/10.1007/s00332-019-09554-3

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