31,906 research outputs found
Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System
This paper is concerned with the traveling wave solutions of an
integro-difference competition system, of which the purpose is to model the
coinvasion-coexistence process of two competitors with age structure. The
existence of nontrivial traveling wave solutions is obtained by constructing
generalized upper and lower solutions. The asymptotic and nonexistence of
traveling wave solutions are proved by combining the theory of asymptotic
spreading with the idea of contracting rectangle
Martingale Problem under Nonlinear Expectations
We formulate and solve the martingale problem in a nonlinear expectation
space. Unlike the classical work of Stroock and Varadhan (1969) where the
linear operator in the associated PDE is naturally defined from the
corresponding diffusion process, the main difficulty in the nonlinear setting
is to identify an appropriate class of nonlinear operators for the associated
fully nonlinear PDEs.
Based on the analysis of the martingale problem, we introduce the notion of
weak solution for stochastic differential equations under nonlinear
expectations and obtain an existence theorem under the H\"older continuity
condition of the coefficients. The approach to establish the existence of weak
solutions generalizes the classical Girsanov transformation method in that it
no longer requires the two (probability) measures to be absolutely continuous.Comment: The new version simplifies some proofs for the main theorems and
generalizes some result
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