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20182026
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math.PR2023

Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method

Kai Du, Zhenjie Ren, Florin Suciu +1

For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measu…

math.PR2020★ 7 cited

Explicit solutions for a class of nonlinear backward stochastic differential equations and their nodal sets

Zengjing Chen, Shuhui Liu, Zhongmin Qian +1

In this paper, we investigate a class of nonlinear backward stochastic differential equations (BSDEs) arising from financial economics, and give specific information about the noda…

math.PR2018

Optimal probabilities and controls for reflecting diffusion processes

Zhongmin Qian, Xingcheng Xu

A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting…

math.PR2018★ 1 cited

Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory

Zhongmin Qian, Xingcheng Xu

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem,…

math.PR2018★ 2 cited

Rough Path Renormalization from Stratonovich to Itô for Fractional Brownian Motion

Zhongmin Qian, Xingcheng Xu

This paper develops an Itô-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons'…