When executing the test below the memory consumption in the Task Manager grows up to 2GB within seconds on my test system - the issue does not occur when the stage style is changed from TRANSPARENT to UNDECORATED.

    public class TransparentStageMemoryIssueTest extends Application  
    {  
      public static void main(String[] args)  
      {  
        Application.launch(args);  
      }  
      @Override  
      public void start(Stage stage)  
      {  
        System.err.println(System.getProperty("javafx.runtime.version"));  
        //stage.initStyle(StageStyle.UNDECORATED);  
        stage.initStyle(StageStyle.TRANSPARENT);  
        final BorderPane root = new BorderPane();  
        root.setStyle("-fx-background-color:#808080;-fx-background-radius:30;-fx-border-radius:30;-fx-border-width:14;-fx-border-color:blue;");  
        Scene scene = new Scene(root, 800, 600);  
        stage.setScene(scene);  
        stage.setX(10);  
        stage.setY(10);  
        stage.show();  
        new Thread()  
        {  
          public void run()  
          {  
            for (int i = 0; i < 1000; i++)  
            {  
              Platform.runLater(new Runnable()  
              {  
                @Override  
                public void run()  
                {  
                  int minSize = 500;  
                  int maxSize = 1000;  
                  int w = minSize + new Random().nextInt(maxSize - minSize);  
                  int h = minSize + new Random().nextInt(maxSize - minSize);  
                  Window win = root.getScene().getWindow();  
                  win.setWidth(w);  
                  win.setHeight(h);  
                }  
              });  
              try  
              {  
                sleep(50);  
              }  
              catch (InterruptedException e)  
              {  
                e.printStackTrace();  
              }  
            }  
          };  
        }.start();  
      }  
    }