Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation

Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation

and Applied Analysis 3 system takes the following form: dxi ⎡ ⎣xi ( ri − bixi − eiyi ) n ∑ j 1 dij ( xj − αijxi ) ⎤ ⎦dt σ1ixidB1i t , dyi yi −γi − δiyi εixi ) dt σ2iyidB2i t , i 1, 2, . . . , n. 1.3 Throughout this paper, we assume dij are nonnegative constants, dij is irreducible, and the parameters ri, γi, bi, ei, δi, εi are positive constants. In order to obtain better dynamic properties of ...

Existence, Uniqueness and Ergodicity of Positive Solution of Mutualism System with Stochastic Perturbation

Stochastic Bandits with Pathwise Constraints

We consider the problem of stochastic bandits, with the goal of maximizing a reward while satisfying pathwise constraints. The motivation for this problem comes from cognitive radio networks, in which agents need to choose between different transmission profiles to maximize throughput under certain operational constraints such as limited average power. Stochastic bandits serve as a natural mode...

Pathwise stationary solutions of stochastic Burgers equations with L[0, 1]-noise and stochastic Burgers integral equations on infinite horizon

In this paper, we show the existence and uniqueness of the stationary solution u(t, ω) and stationary point Y (ω) of the differentiable random dynamical system U : R×L[0, 1]×Ω → L[0, 1] generated by the stochastic Burgers equation with L[0, 1]-noise and large viscosity, especially, u(t, ω) = U(t, Y (ω), ω) = Y (θ(t, ω)), and Y (ω) ∈ H[0, 1] is the unique solution of the following equation in L[...

Pathwise Stochastic Control Problems and Stochastic

In this paper we study a class of pathwise stochastic control problems in which the optimality is allowed to depend on the paths of exogenous noise (or information). Such a phenomenon can be illustrated by considering a particular investor who wants to take advantage of certain extra information but in a completely legal manner. We show that such a control problem may not even have a “minimizin...