Averaging principle for the heat equation driven by a general stochastic measure

Strong Convergence Rate in Averaging Principle for the Heat Equation Driven by a General Stochastic Measure

“…Also we can compare our estimate in (3.5) with results of other papers. In [19], for for equations (3.1) and (3.4), for f independent of t, it was proved that we can take any 0…”

“…A similar problem was recently studied in [19], but in that paper function f in (1.1) did not depend on the time variable, and averaging was considered for a stochastic term only. Note that the convergence rate obtained in [19] is higher that rate in the given paper (see Remark 3.2 below).…”

Averaging principle for fractional heat equations driven by stochastic measures

“…Recently, in [9], Vadym Radchenko investigated a class of stochastic heat equations driven by a stochastic measure µ, wherein the stochastic measure µ only satisfies the σ-additivity in probability (see the precise description in Section 2). Moreover, the same author established in [10] an averaging principle for such equations. Motivated by the above results, in this short paper, we want to consider an averaging principle for the following equation…”

The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises

“…In case with Poisson random measure was studied in Pei et al [12] and α-noise in Bao et al [13]. An averaging principle for the heat equation driven by a general stochastic measure was studied by Radchenko [14].…”