In Leo Tolstoy's novel Anna Karenina (1873-1877), there's a point where the author refers to a "new doctrine" that was fashionable among the Russian upper classes. The following extract is from Part 5, Chapter 22 (translated by Nathan Haskell Dole, 1899), in which Anna's husband Alexei is comforted by Lidia Ivanovna.
"How can you be ashamed of what is the highest degree of Christian perfection? He who humbles himself shall be exalted. And you cannot thank me. Thank Him, pray to Him for help. In Him alone we can find peace, consolation, salvation, and love".
She raised her eyes to heaven, and began to pray, as Alexei Aleksandrovitch could see by her silence.
Alexei Aleksandrovitch listened to her, and this phraseology, which before seemed, not unpleasant to him, but extravagant, now seemed natural and soothing. He did not approve of this new ecstatic mysticism. He was a sincere believer, and religion interested him principally in its relation to politics; and the new doctrine which arrogated to itself certain terms, for the very reason that it opened the door to controversy and analysis, had aroused his antipathy from principle.
But nevertheless, the countess's help was to the highest degree useful to him. Her affection and esteem were a moral support to him, and, as it gave her great consolation to think, she almost succeeded in converting him to "Christianity"; in other words, she changed him from an indifferent and lukewarm believer into a fervent and genuine partizan of that new method of explaining the Christian doctrine which shortly after came into vogue in Petersburg. It was easy for Alexei Aleksandrovitch to put his faith in this exegesis. [...] Thus he saw no impossibility or unlikelihood in death existing for unbelievers and not for him, that because he held a complete and unquestioning faith, judged in his own way, his soul was already free from sin, and that even in this world he might look upon his safety as assured.
It is true, Alexei Aleksandrovitch dimly felt the frivolity, the fallacy, of this presentation of the faith.
Which particular "new doctrine" and movement is Tolstoy referring to? It is described as having a mystic element, evidently with some connection to humility and prayer, and also, for believers alone, the assurance of salvation, with a form of perfectibility or sinlessness.
Tolstoy himself refers to it as frivolous and fallacious, so presumably it diverges from his own religious views; it's also evidently not the mainstream position of the Russian Orthodox Church. Historically speaking, we are in late nineteenth-century Russia, among the upper crust of society, and perhaps in St Petersburg specifically.