The word refers (obviously) to that one thing that seemed to point to whatever God was doing in your life. That which you felt was only for you and maybe showed up in a dream. A little detail that when boiled down to its elements, meant something symbolic and stood out in your mind upon reflection. Does anything come to mind?
"In all Thy ways, acknowledge Him..." (Proverbs 3:6)
In reality, the word stochastic actually exists. Statistically speaking, it refers to a set of parts, lots of them, that look for all intents and purposes, like a bunch of randomness doing its thing. A stochastic exposition on the randomness you've observed can only be done in retrospect, I should add. Extrapolate this notion out to the whole of life and that is indeed what a lot of it (life) outside ours looks to be: random. Cars driving down the road, making their way to and from God knows where (if you think about it, pray for the drivers). Zoom in. That red car driving by. You don't recognize the driver, but just before coming to a stop at the light, you noticed the plate bore some number corresponding with the scripture God had on your heart today. This means something, but what? Nothing? It doesn't mean anything. You turn your collar up and keep walking. What's that you say? You had a dream about the same? When...? Last night? Because if you dreamed about such odd details after the fact, I could see how some meaning might emerge. Some meaning to you and no one else. Heh. Think what you'd do if you ever met the driver. You could run up to them as they got out of their car and spill this whole story to them. And they'd walk away thinking you're crazy. But you're not crazy. You feel God is speaking to you. It's like a language that utilizes everything as opposed to mere letter and sound.
"Incline not my heart to any evil thing, to practise wicked works with men that work iniquity: and let me not eat of their dainties." (Psalm 141:4)
And here's the stochasm. Falling into these minor details that—while truly random—will get your eyes off God and on that which He wants you to focus. Namely, Him. I must admit, I am very perceptive. I notice things and also I think everyone else sees the same stuff I do. This is wrong. While I believe in God and along with that, believe He indeed does see everything, I can't tell you what others are paying attention to. This would mean I would need another person's opinion as to what I see and feel. And if I'm pressed in to God, I don't.
"And it came to pass at the seventh time, that he said, Behold, there ariseth a little cloud out of the sea, like a man's hand. And he said, Go up, say unto Ahab, Prepare thy chariot, and get thee down, that the rain stop thee not." (1 Kings 18:44, emphasis mine)
Another definition of stochastic is as follows: "the random variable". That one part out of the whole that was the focal or turning point for the equation. Here's the thing about God. If you're waiting for deep and powerful things from Him—the answers of which involve more than just you and yours—you must look out for these signs. Assuming your heart and motives are right, God will show you things, signs and symbols in the natural, physical world that herald the answers to your prayer and waiting. But it doesn't necessarily have to directly correlate to your blessing as a "little cloud...like a man's hand" does to "rain". You follow me?