In the paper, we consider the limit behavior of partial-sum random field (r.f.) \( \left.{S}_n\left({t}_1,{t}_2;\right)X\left(b\left(\mathbf{n}\right)\right)\right)={\sum}_{k=1}^{\left[{n}_1{t}_1\right]}{\sum}_{l=1}^{\left[{n}_2{t}_2\right]}{X}_{k,l}\left(b\left(\mathbf{n}\right)\right), \) where \( \left\{{X}_{k,l}\left(b\left(\mathbf{n}\right)\right)={\sum}_{i=0}^{\infty }{\sum}_{j=0}^{\infty }{c}_{i,j}{\upxi}_{k-i,l-j}\left(b\left(\mathbf{n}\right)\right),k,l\in \mathrm{\mathbb{Z}}\right\},n\ge 1, \) is a family (indexed by n = (n₁, n₂), n_i ≥ 1) of linear r.f.s with filter c_i,j = a_ib_j and innovations ξ_k,l(b(n)) having heavy-tailed tapered distributions with tapering parameter b(n) growing to infinity as n → ∞. In [V. Paulauskas, Limit theorems for linear random fields with tapered innovations. I: The Gaussian case, Lith. Math. J., 61(2):261–273, 2021], we considered the so-called hard tapering as b(n) grows relatively slowly and the limit r.f.s for appropriately normalized S_n(t₁, t₂;X(b(n))) are Gaussian. In this paper, we consider the case of soft tapering where b(n) grows more rapidly in comparison with the case of hard tapering and stable limit r.f.s.We consider cases where the sequences {a_i} and {b_j} are long-range, short-range, and negatively dependent.

在论文中，我们考虑了部分和随机场 (rf) \( \left.{S}_n\left({t}_1,{t}_2;\right)X\left(b\left (\mathbf{n}\right)\right)\right)={\sum}_{k=1}^{\left[{n}_1{t}_1\right]}{\sum}_{l =1}^{\left[{n}_2{t}_2\right]}{X}_{k,l}\left(b\left(\mathbf{n}\right)\right), \)其中\( \left\{{X}_{k,l}\left(b\left(\mathbf{n}\right)\right)={\sum}_{i=0}^{\infty } {\sum}_{j=0}^{\infty}{c}_{i,j}{\upxi}_{ki,lj}\left(b\left(\mathbf{n}\right)\ right),k,l\in \mathrm{\mathbb{Z}}\right\},n\ge 1, \)是一个族（由n  = ( n ₁ ,  n ₂ ),  n _i  ≥  1索引）带有滤波器c _i,j的线性 rfs= a _i b _j和创新ξ _k,l ( b ( n )) 具有重尾锥形分布，锥形参数b ( n ) 随着n → ∞增长到无穷大。在 [V. Paulauskas，具有锥形创新的线性随机场的极限定理。I：高斯情况，Lith。数学。J. , 61(2):261–273, 2021]，我们考虑了所谓的硬锥形，因为b ( n ) 增长相对缓慢，并且适当归一化的S _n ( t ₁ , t ₂ ; X( b ( n ))) 是高斯分布的。在本文中，我们考虑了软锥化的情况，其中b ( n ) 与硬锥化和稳定极限 rfs 的情况相比增长得更快我们考虑了序列 { a _i } 和 { b _j } 是长程的情况，短程，负相关。