arXiv subjects

Yingting Miao

Publications and source records attributed to Yingting Miao.

4 recordsLinked to original sources

arXiv2026

Pseudo-differential noise and nonlocal singularity formation in the stochastic Córdoba--Córdoba--Fontelos equation

We study the stochastic Córdoba--Córdoba--Fontelos equation driven by multiplicative Stratonovich noise. The noise amplitude is allowed to be a pseudo-differential operator whose leading part is nearly skew-adjoint. This class contains classical transport noise and also permits genuinely nonlocal perturbations. We first develop a local-in-time theory for maximal classical solutions in Sobolev spaces, proving existence, uniqueness, and a blow-up criterion. We then consider the special case of Stratonovich transport. For sufficiently large initial nonlocal steepness at a global maximum, we prove finite-time blow-up with arbitrarily high prescribed probability and obtain an explicit upper bound on the lifespan. Finally, on the event that the nonlocal steepness at the transported maximum diverges, we establish a conditional Type-I upper bound. When the terminal Cesàro average of the normalised nonlocal energy converges, we further identify the exact leading-order blow-up rate in terms of its limiting value.

math.AP↗

arXiv2026

Optimal Investment and Consumption Strategies with General Cost Structure under CRRA Utility

Transaction costs play a critical role in portfolio allocation and consumption decisions. We study a finite-horizon consumption--investment problem with CRRA utility under a general class of transaction cost functions. Based on dynamic programming and a singular perturbation expansion for a small cost-to-wealth ratio, we derive leading-order asymptotic formulas for the no-trade region, the four trading boundaries, the value function correction, and the optimal consumption rate. We further show how fixed, proportional, fixed-plus-proportional, and nonlinear transaction costs arise as special cases of the general framework. The results show that the leading-order no-trade region is governed by the fixed and proportional components, while the framework still accommodates nonlinear cost structures. Complementing the asymptotic analysis, we prove a verification theorem for the exact impulse-control formulation under a strictly positive fixed cost component, and characterize its limiting transitions to singular and continuous control regimes as the fixed cost vanishes.

q-fin.PM↗

arXiv2023

Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities

This paper aims at studying a generalized Camassa--Holm equation under random perturbation. We establish a local well-posedness result in the sense of Hadamard, i.e., existence, uniqueness and continuous dependence on initial data, as well as blow-up criteria for pathwise solutions in the Sobolev spaces $H^s$ with $s>3/2$ for $x\in\mathbb{R}$. The analysis on continuous dependence on initial data for nonlinear stochastic partial differential equations has gained less attention in the literature so far. In this work, we first show that the solution map is continuous. Then we introduce a notion of stability of exiting time. We provide an example showing that one cannot improve the stability of the exiting time and simultaneously improve the continuity of the dependence on initial data. Finally, we analyze the regularization effect of nonlinear noise in preventing blow-up. Precisely, we demonstrate that global existence holds true almost surely provided that the noise is strong enough.

math.AP↗

arXiv2022

Global existence and blow-up for a stochastic transport equation with non-local velocity

In this paper we investigate a non-linear and non-local one dimensional transport equation under random perturbations on the real line. We first establish a local-in-time theory, i.e., existence, uniqueness and blow-up criterion for pathwise solutions in Sobolev spaces $H^{s}$ with $s>3$. Thereafter, we give a complete picture of the long time behavior of the solutions based on the type of noise we consider. On one hand, we identify a family of noises such that blow-up can be prevented with probability $1$, guaranteeing the existence and uniqueness of global solutions almost surely. On the other hand, in the particular linear noise case, we show that singularities occur in finite time with positive probability, and we derive lower bounds of these probabilities. To conclude, we introduce the notion of stability of exiting times and show that one cannot improve the stability of the exiting time and simultaneously improve the continuity of the dependence on initial data.

math.AP↗