This paper investigates a class of distributed fractional-order stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2<H<1. By employing the Picard iteration method, we rigorously prove existence and uniqueness solutions Lipschitz conditions. Furthermore, leveraging Girsanov transformation argument within L2 metric framework, derive quadratic transportation inequalities for law strong solution to considered equations. These results provide...

The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged the original proposed, as well their solutions are quantitatively compared. Under some appropriate assumptions, to systems can be approximated by stochastic in sense of mean square.

This paper develops a new method to deal with the problem of identifying unknown source in Poisson equation. We obtain regularization solution by Tikhonov super-order penalty term. The order optimal error bounds can be obtained for various smooth conditions when we choose parameter discrepancy principle and process is uniform. Numerical examples show that proposed effective stable.

Abstract This manuscript focuses on a class of stochastic functional differential equations driven by time-changed Brownian motion. By utilizing the Lyapunov method, we capture some sufficient conditions to ensure that solution for considered equation is η -stable in p th moment sense. Subsequently, present new criteria -stability mean square using Itô formula and proof contradiction. Finally, provide examples demonstrate effectiveness our main results.

In this paper, we classify $3$-dimensional complete self-shrinkers in Euclidean space $\mathbb R^{4}$ with constant squared norm of the second fundamental form $S$ and $f_{4}$.

Being base on the Girsanov theorem for multifractional Brownian motion, which can be constructed by derivative operator, we establish Harnack inequalities a class of stochastic functional differential equations driven subordinate motion an approximation technique.

<abstract><p>In this paper, we investigate a class of stochastic functional differential equations driven by the time-changed Lévy process. Using Lyapunov technique, obtain some sufficient conditions to ensure that solutions considered are $ h $-stable in p $-th moment sense. Subsequently, using Itô formula and proof reduction ad absurdum, capture new criteria for $-stability mean square equations. In end, analyze illustrative examples show interest usefulness major...

<abstract><p>Uncertain differential equation is a type of driven by canonical Liu process. By applying some uncertain theories, the sufficient conditions exponential stability in mean square obtained for nonlinear equations. At same time, new criteria ensuring existence global attracting sets considered equations are presented.</p></abstract>

Abstract In this paper, we deal with a new type of differential equations called generalized anticipated backward doubly stochastic (GA-BDSDEs). The coefficients these BDSDEs depend on the future value solution <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>Y</m:mi> <m:mo>,</m:mo> <m:mi>Z</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> ${(Y,Z)}$ . We obtain an existence and uniqueness theorem comparison for reflected solutions equations.

In this paper, we consider the existence and uniqueness of mild solution for a class coupled fractional stochastic evolution equations driven by Brownian motion with Hurst parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>H</mml:mi><mml:mo>∈</mml:mo><mml:mfenced open="(" close=")"...

In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $α$-regular Volterra process. Based on equivalence between and evolution equation, get equations.