The October Revolution also inspired the building of Welfare States in the capitalist world.
Not really. The Depression and the War are far more responsible for that. You're not going to see much of a welfare state constructed in the 1920s in the aftermath of the Bolshevik seizure of power in Russia.
Not entirely down to the depression though - many countries were already beginning to put the first elements of the welfare state together in the first decades of the 20th Century. For example, Britain was already introducing unemployment insurance and the old age pension in the 1910s, Switzerland was already nationalising key parts of its infrastructure and so on.
A lot of this was moralistic 19th century "muscular liberalism", but these moves also did happen in part as a result of the governing elite trying to stave off socialism at home. So maybe not a result of the Bolshevik revolution - but definitely a result of the fear of a socialist revolt.
