Convergence of switching diffusions

This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on semimartingale techniques, so that no Markovian assumption for the modulating process is needed

Backward stochastic variational inequalities with locally bounded generators

The paper deals with the existence and uniqueness of the solution of the backward stochastic variational inequality: \begin{equation} \left\{\begin{array} {l}-dY_{t}+\partial \varphi(Y_{t})dt \ni F(t,Y_{t},Z_{t})dt-Z_{t}dB_{t},\;0\leq t<T \\ Y_{T}=\eta, \end{array} \right.\end{equation} where $F$ satisfies a local boundedness condition.Comment: Minor edits and a slight change to title have been mad

Model tracking for risk problems

We assume that we have M candidate insurance models for describing a process. The models considered consist of a risk process driven by right-constant, finite-state spaces, jump processes. Based on observing the history of the risk process, we propose dynamics whose solutions indicate the likelihoods of each candidate model

Stochastic Averaging Principle for Dynamical Systems with Fractional Brownian Motion

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their solutions are quantitatively compared. It is shown that the solution of the averaged SDE converges to that of the original SDE in the sense of mean square and also in probability. It is further demonstrated that a similar averaging principle holds for SDEs under stochastic integral of pathwise backward and forward types. Two examples are presented and numerical simulations are carried out to illustrate the averaging principle