Dice simulation and counting pairs
Minor things

The java naming standard for classes is CamelCase (DiceSimulation instead of diceSimulation)

A constant of THOUSAND is not helpful, especially when the value is 10,000. A more meaningful name, say ROLLCOUNT, would be better.

Similarly, diceValue is not clear.  It contains the counts for each double occurence, so perhaps, doubleCounts - note the plural for an array indicating that it contains multiple values.

We have many dice but each one is a die -> die1 and die2.

Comments that just restate the obvious code can be omitted 
e.g.

/**
* Declare variables and store dice max roll in Thousand
*/

// create new instance of random 

// If statement to check if values are the same or not


Coding

We are working with 6 sided dice so we only need 6 entries in the array to store the double counts not 7 - it is more standard to adjust the index when outputting (e.g., add 1) than to make the arrays larger and use then as 1 based arrays..

We can easily store the number of sides in a variable (constant) to make consistency easier - a named value instead of a literal 6 in multiple places - and even allow us to use this for dice with other numbers of sides if we desired.

We can put the 'roll' functionality into a function so that to reduce duplication and allow us to change the implementation if desired (say for testing)

We check if dice1 == dice2 but then in the loop check if both dice1 == i &amp;&amp; dice2 == i - if dice1 == dice2 then the second check can never fail.

If we index into the array, we don't need the loop 

if (die1==die2){
    doubleCounts[die1-1]++;
}


If have sized the array to the number of elements then we should loop from 0 not 1 (and single character variable names, even for loops, are generally frowned upon)

System.out.format is a nicer way - simpler to use than the concatenation - for writing the output line

import java.util.*;

public class DiceSimulation {

    private static Random rollDice = new Random();

    public static void main(String[] args) {

        final int ROLLCOUNT = 10000;
        final int SIDES = 6;
        int counter, die1, die2;

        //an array with elements to keep count
        int [] doubleCounts = new int [SIDES];

        // display welcome message. no other purpose but trial
        welcome ();

        /**
         * Set counter to start from 1 and go till desired constant number
         * Rolling two separate dices and storing values in dice1 &amp; dice 2       respectively
         */
        for (counter=1; counter&lt;=ROLLCOUNT;counter++){

            die1=roll(SIDES);
            die2=roll(SIDES);

            if (die1==die2){
                doubleCounts[die1-1]++;
            }

        }

        // Display results totals of paired rolls 
        for (int idx=0; idx&lt;doubleCounts.length; idx++){
            System.out.format(" You rolled set of %d %d times\n",(idx+1), doubleCounts[idx]);
        }
    }
    private static int roll(int sides){
        return rollDice.nextInt(sides) +  1;
    }
    public static void welcome () {
        System.out.println("welcome to dice world!");
    }
}