{"title":"On near-martingales and a class of anticipating linear stochastic differential equations","authors":"Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha, Padmanabhan Sundar","doi":"10.1142/s0219025723500297","DOIUrl":null,"url":null,"abstract":"<p>The goals of this paper are to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. For a class of anticipating linear stochastic differential equations, we prove the existence and uniqueness of solutions using two approaches: (1) Ayed–Kuo differential formula using an ansatz, and (2) a braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin–Wentzell type large deviations result for the solution of such equations. In addition, we prove large deviation results for small noise where the initial conditions are random.</p>","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"37 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infinite Dimensional Analysis Quantum Probability and Related Topics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219025723500297","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The goals of this paper are to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. For a class of anticipating linear stochastic differential equations, we prove the existence and uniqueness of solutions using two approaches: (1) Ayed–Kuo differential formula using an ansatz, and (2) a braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin–Wentzell type large deviations result for the solution of such equations. In addition, we prove large deviation results for small noise where the initial conditions are random.
期刊介绍：
In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields.
It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
