Remarks on Stochastic Systems I: Markov properties, local and global uniqueness, and limits of stochastic equations

2022/09/13 by Seiichiro Kusuoka, Kusuoka, Seiichiro
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2209.05961

openalex publication_date 2022/09/13 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/28

Abstract

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we show that such stochastic differential equations appear in the limits of stochastic differential equations which have the existence and pathwise uniqueness of solutions. These examples are constructed in motivation to singular stochastic partial differential equations. We also give some examples of shifted equations whose sum of the solutions depends on the choices of the decomposition of the initial condition of the original equation.

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