I was wondering about the relation or influence that Stoicism had on Existentialism and Existentialist thinkers, such as Camus, Nietzsche, Kierkegaard, and Sartre.
In any of their works do they reference any Stoics or Stoic works?
I'm far more familiar with Stoic works than I am works of the Existentialists.
NIETZSCHE AND THE STOICS
A major point of difference between Nietzsche and the Stoics in regard to the role of the emotions is something you might care to condsider. For a first look at the difference consider the following (read past the references to Spinoza, interesting but not for your purposes) :
This article reviews the influence of Stoic thought on the development of Spinoza’s and Nietzsche’s ethics and suggests that although both philosophers follow the Stoics in conceiving of ethics as a therapeutic enterprise that aims at human freedom and flourishing, they part company with Stoicism in refusing to identify flourishing with freedom from the passions. In making this claim, I take issue with the standard view of Spinoza’s ethics, according to which the passions figure exclusively as a source of unhappiness and bondage from which we must be liberated. I argue that, in fact, Spinoza anticipates Nietzsche and breaks with the Stoics in offering a more positive assessment of the role of passionin a flourishing life. The reading pursued here takes Spinoza’s divergence from the Stoic account of the passions to be a consequence of his insistence on the immanence of human being in nature. I outline Spinoza’s and Nietzsche’s conception of immanence and suggest that it entails a common understanding of our nature as dynamic power or desire, which is simultaneously expressed as a capacity to act and be acted on, to affect and to be affected. The recognition of the complex relationship between passive and active power requires a revaluation of our vulnerability and openness to what can affect us and leads each philosopher to a consideration of the ways in which the passions might be made to support our striving to increase our power and to realize an essentially limited freedom and precarious flourishing. (Aurelia Armstrong, The Passions, Power, and Practical Philosophy Spinoza and Nietzsche Contra the Stoics', Journal of Nietzsche Studies, Vol. 44, No. 1, Special Issue: Nietzsche and the Affects (Spring 2013), pp. 6-24 - quotation from p.6.)
Given his background as a classical scholar, any direct with the Stoics is more likely to run through the Nietzschw than through the other writers you mention. But there is something in Kierkegaard :
KIERKEGAARD AND THE STOICS
He shows no understanding of Abraham in Fear and Trembling, none of Antigone in Either / Or, none of Solomon in Stages on Life's Way: he always writes about himself. His brilliant sketch of "Stoic" defiance in The Sickness Unto Death is such that SK himself is driven to admit that "this sort of despair is seldom seen in the world." (206) When he adds, "Nevertheless such a despairer is to be met with also in real life," we are served notice that he projects himself, as if that did not go without saying. SK's strange Stoic does not doubt God, has no qualms about the meaning of "God," but out of sheer pride refuses obedience. It is, SK says, as if a "clerical error would revolt against the author, out of hatred for him were to forbid him to correct it, and were to say, 'No, I will not be erased, I will stand as a witness against thee, that thou art a very poor writer.' Being physically deformed, SK knew the temptation of flinging himself into the face of God with words like these; and for him obedience to God meant humble acceptance of the absurd. (Walter Kaufmann, 'Kierkegaard', The Kenyon Review, Vol. 18, No. 2 (Spring, 1956), pp. 182-211 - quotation from p.192.)
POSTSCRIPT
Virmaior's comments and advice are as always excellent; I have separated Nietzsche and Kierkegaard from the others. There would not be room in any case to provide an adequate answer for all the philosophers you mention.
Stoicism is a form of attaining self authenticity through the rejection of own dreams and impossible plans, for the sake of acceptance of and reconciliation with painful conditions, whereby one exercises controls over only what he has power to control. Stoic is free when he is busy with controlling own passions while the world out there is beyond his control.
Sartre was distressed when he was mobilized on war in September 39. He was anxious with the perspective to be killed without having done anything great in his life. Under the impression produced by reading Heidegger he was all in the search of an "authentic position" in front of the face of danger. He first inclined towards becoming a stoicist (read "Notebooks from a Phoney War").
For Sartre that meant to quit his self-identification as a man meant to become great with his writings one day, and to put on sincerely the role of a soldier without love and future, meant to die.
While being in the army in 1939, and later in a camp for prisoners of war in 1940, he felt increasingly dissatisfied with the ostrich head-in-sand, "passive" (albeit of endurance) self-positioning. He began to strenghthen in his concept according to which everything we experience (including negative feelings) has been pre-processed and taken on by our (pre-reflective) consciousness, that everything can affect us not otherwise than only through us and via our "stamp". Therefore, if I feel e.g. helpless it is due to myself, my choice to be so. Thus, a man is responsible for everything which happens with him.
Sartre specially stipulates that the responsibility is not obvious to the first person perspective - not only because the choice is unreflective but also because it is not based on anything: consciousness is the basis of its possibilities and choices while consciousness itself exists by no ground; he labels this paradoxic yet fundamental human condition "unbearable" - since a man looks sentenced to be responsible for what happens with him in a way like he's just a receiver.
But as long as own reaction has been self-selected and the one is responsible for it the one ought to consciously charge himself with it as if it was voluntary chosen on purpose and as if for some progress to make about oneself. ("Notebooks from...", Mon., Dec. 4.)
There cannot be a world apriori/knowingly beyond control, because we can find ourselves only in such a world where our finger is in the pie already.
This existentialistic stance made Sartre a soldier/captive more active than he was initially under his stoicism. A stoicist will restrict himself with doing things he feels to be in control of; a Sartrian will expand himself doing things as if his circumstances are the condition of the whole world and are what he had brought in willingly, whatever is his control radius (the control and power will then get corrected via practical acts).
