The default WPF behavior is that your implicit ScrollBar style would apply to the scrollbars in the ListBox. If this is not occurring in your application then there is something overriding this default behavior. Do you have a Template applied to the ListBox?
My test app to prove out the default styling behavior is below:
<Window x:Class="TestScrollBarStyle.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Window.Resources>
<Style TargetType="ScrollBar">
<Setter Property="Background" Value="Red" />
</Style>
</Window.Resources>
<Grid>
<Grid.RowDefinitions>
<RowDefinition />
<RowDefinition />
</Grid.RowDefinitions>
<ScrollViewer x:Name="scroll">
<Rectangle Height="200" />
</ScrollViewer>
<ListBox Grid.Row="1" ScrollViewer.VerticalScrollBarVisibility="Visible">
<ListBoxItem>Test 1</ListBoxItem>
<ListBoxItem>Test 2</ListBoxItem>
<ListBoxItem>Test 3</ListBoxItem>
<ListBoxItem>Test 4</ListBoxItem>
<ListBoxItem>Test 5</ListBoxItem>
<ListBoxItem>Test 6</ListBoxItem>
<ListBoxItem>Test 7</ListBoxItem>
<ListBoxItem>Test 8</ListBoxItem>
<ListBoxItem>Test 9</ListBoxItem>
<ListBoxItem>Test 10</ListBoxItem>
<ListBoxItem>Test 11</ListBoxItem>
</ListBox>
</Grid>