Exit times in non-Markovian drifting continuous-time random walk processes

关于消耗战型 Dynkin 博弈中马尔可夫随机化均衡的存在性

On the existence of Markovian randomized equilibria in Dynkin games of war-of-attrition-type

本文针对消耗战型非零和 Dynkin 博弈，通过构建马尔可夫随机化停止时间的适当拓扑，证明了马尔可夫完美均衡的存在性，填补了随机化情形下马尔可夫停止博弈均衡理论的空白。

一个退出合约优化问题

An exit contract optimization problem

本文研究面向多个异质代理人的通用退出合约设计问题，利用Bank-El Karoui表示将其转化为最优控制与多重停时问题，证明最优合约存在，并给出离散时间逼近及马尔可夫/连续合约类上的讨论。

Backward Stochastic Differential Equations with Non-Markovian Singular Terminal Conditions with General Driver and Filtration

We consider a class of Backward Stochastic Differential Equations with superlinear driver process $f$ adapted to a filtration supporting at least a $d$ dimensional Brownian motion and a Poisson random measure on ${\mathbb R}^m- \{0\}.$ We consider the following class of terminal conditions $ξ_1 = \infty \cdot 1_{\{τ_1 \le T\}}$ where $τ_1$ is any stopping time with a bounded density in a neighborhood of $T$ and $ξ_2 = \infty \cdot 1_{A_T}$ where $A_t$, $t \in [0,T]$ is a decreasing sequence of events adapted to the filtration ${\mathcal F}_t$ that is continuous in probability at $T$. A special…

First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface

We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both directions Gaussian interface. We show that Q_t decays when t \to \infty as a power-law $^{-1 - α}, where αis non-universal and proportional to the ratio of the thermal energy and the elastic energy of a fluctuation of size L. The fact that αappears to be dependent on L, which is rather unusual, implies that the number of existing moments of Q_t depends on …

The first passage problem for stable linear delay equations perturbed by power law Lévy noise

This article studies a linear scalar delay differential equation subject to small multiplicative power tail Lévy noise. We solve the first passage (the Kramers) problem with probabilistic methods and discover an asymptotic loss of memory in this non-Markovian system. Furthermore, the mean exit time increases as the power of the small noise amplitude, whereas the pre-factor accounts for memory effects. In particular, we discover a non-linear delay-induced exit acceleration due to a non-normal growth phenomenon. Our results are illustrated in the well-known linear delay oscillator driven by $α$-…

Brownian-Time Processes: The PDE Connection and the Half-Derivative Generator

We introduce a class of interesting stochastic processes based on Brownian-time processes. These are obtained by taking Markov processes and replacing the time parameter with the modulus of Brownian motion. They generalize the iterated Brownian motion (IBM) of Burdzy and the Markov snake of Le Gall, and they introduce new interesting examples. After defining Brownian-time processes, we relate them to fourth order parabolic PDEs. We then study their exit problem as they exit nice domains in $\Rd$, and connect it to elliptic PDEs. We show that these processes have the peculiar property that they…