From a search of two keywords of your subject in the Processing.org search box:
https://www.google.com/search?as_sitesearch=processing.org&as_q=transparent+frame

I have an old sketch showing some possibilities:
http://bazaar.launchpad.net/~philho/+junk/Processing/view/head:/_QuickExperiments/_Java/WindowTransparency/WindowTransparency.pde

But curiously, in 2.0b6, while it works, the sketch isn't updated / animated (works in 1.5.1).

I made a version working...
While it is very easy in pure Java, Processing makes it hard by setting the frame in a state that is hard to get rid of.
The solution, given by xavierv1, is to hide the main frame and to create a new one, unencumbered by these issues.
It isn't great, because animation makes the window to flicker a lot, even more if the window is bigger...
Well, here it is:

1. // Making a translucent and shaping window in Processing
2. // https://blogs.oracle.com/thejavatutorials/entry/translucent_and_shaped_windows_in
3. // and
4. // https://forum.processing.org/topic/translucen-window-in-processing
5. // to apply to Processing (gave the trick to use a secondary frame)
6.  
7. import javax.swing.JFrame;
8.  
9. final java.awt.Color fullyTransparent = new java.awt.Color(0, 0, 0, 0);
10.  
11. // Apparently, Processing forces a background, and we cannot override it,
12. // so we have to hide the Processing's frame, and make our own
13. JFrame displayedFrame;
14. Frame oldFrame;
15.  
16. public void init()
17. {
18.   oldFrame = frame;
19. //  frame.setLocation(-5000, -5000);
20.   /*
21.   // Hide the old frame
22.   frame.removeNotify();
23.   frame.setUndecorated(true);
24. //  frame.setOpacity(0.8);
25.   frame.setBackground(fullyTransparent);
26.   frame.addNotify();
27.   //*/
28.  
29.   //*
30.   displayedFrame = new JFrame();
31.   displayedFrame.removeNotify();
32.   displayedFrame.setUndecorated(true);
33.   displayedFrame.setLayout(null); // Each added component replace the previous one
34.   displayedFrame.setLocationRelativeTo(null);
35.   displayedFrame.setLocation(200, 200);
36. //  displayedFrame.setOpacity(1);
37.   displayedFrame.addNotify();
38.  
39.   frame = displayedFrame;
40. //  displayedFrame.add(this);
41.   //*/
42.  
43.   super.init();
44.   
45.   // Allow transparency on the sketch's main graphics
46.   g.format = ARGB;
47.   // Tell it isn't the primary drawing surface (even if it is), to avoid automatic background() call
48.   g.setPrimary(false);
49. }
50.  
51. final int MARGIN = 25;
52.  
53. void setup()
54. {
55.   size(300, 200); // Flickers more with a bigger window...
56.   smooth();
57.  
58.   //*
59.   displayedFrame.setSize(width, height);
60.   // The size must be set before
61.   displayedFrame.setBackground(fullyTransparent);
62.   displayedFrame.setVisible(true);
63.   //*/
64.  
65.   posX = width / 2;
66.   posY = height / 2;
67. }
68.  
69. void clearBackground()
70. {
71.   loadPixels();
72.   Arrays.fill(pixels, 0x100000FF);
73.   updatePixels();
74. }
75.  
76. float posX, posY;
77. void draw()
78. {
79.   // Must be called in draw(), for some unknown reason... And on the second frame!
80.   if (frameCount == 2) oldFrame.setVisible(false);
81. //  clearBackground();
82.   background(0, 0, 50, 50);
83.  
84.   color c = #2222FF;
85.   int w = width - 1;
86.   int h = height - 1;
87.   strokeWeight(1);
88.   for (int i = 0; i < MARGIN; i++)
89.   {
90.     stroke(c, i * 100.0 / MARGIN);
91.     line(i, i + 1, i, h - i - 1);
92.     line(w - i, i + 1, w - i, h - i - 1);
93.     line(i, i, w - i, i);
94.     line(i, h - i, w - i, h - i);
95.   }
96.   fill(c, 100);
97.   noStroke();
98.   rect(MARGIN, MARGIN, w - 2 * MARGIN + 1, h - 2 * MARGIN + 1);
99.  
100.   stroke(#EEEE00);
101.   strokeWeight(8);
102.   fill(#AAFF44);
103.   posX += random(-1, 1);
104.   posY += random(-1, 1);
105.   ellipse(posX, posY, height / 3, height / 3);
106.   
107.   noFill(); noStroke();
108. //  stroke(#FFFF00); strokeWeight(1); rect(0, 0, w, h);
109.  
110.   // We need to do this on each frame to get the animation... 
111.   displayedFrame.add(this);
112. }
113.  
114. // Dragging the frame
115. int mX;
116. int mY;
117.  
118. void mousePressed()
119. {
120.   mX = mouseX;
121.   mY = mouseY;
122. }
123.  
124. void mouseDragged()
125. {
126.   java.awt.Point p = java.awt.MouseInfo.getPointerInfo().getLocation();
127.   frame.setLocation(p.x - mX, p.y - mY);
128. }