time $ t=h $ at the point $ x' $, which the particle reaches by a jump from the point $ x $, and $\tilde{\eta}_{t}^{1}(y), \ldots , \tilde{\eta}_{t}^{n}(y) $ are independent processes born in time $h$, produced by $n$ offsprings of the initial particle.

From above, it follows that $$\begin{gathered}
\label{E1.3}
\left| \frac{ F_{1}(z; t+h, x, y) -  F_{1}(z; t, x, y)} {h}  - (\mathscr{A}F_{1}(z; t, \cdot, y))(x) + \delta_{0}(x)f(F_{1}(z; t, x, y)) \right| \\
\leqslant \sum_{x'\neq x} \left|  \frac{p(h, x, x')}{h} - a(x, x') \right|  + \sum_{n\neq 1} \left|  \frac{p_{*}(h, n)}{h} - b_n \right| \\
+ \left| \frac{p(h, x, x)}{h} - \frac{1}{h} - a(x,x) \right|  + \left| \frac{p_{*}(h, 1)}{h} - \frac{1}{h} -a(0,0) - b_1 \right|.
 \end{gathered}$$

The last two summands on the right side of equation  tend to zero when $h \to 0$ in view of  and . Fix an arbitrary $ K > 0 $ and estimate the first summand on the right side of equation : $$\begin{gathered}
\label{I1}
\sum_{x'\neq x} \left|  \frac{p(h, x, x')}{h} - a(x, x') \right|
\leqslant \sum_{0 < | x' - x| \leqslant K} \left|  \frac{p(h, x, x')}{h} - a(x, x') \right|\\  + \sum_{| x' - x| > K} a(x, x')  + \sum_{| x' 