The dollar marched higher against the euro and yen on Monday as investors wagered that interest rates were set on a diverging course in the United States, Europe and Japan, giving a lift to Tokyo stocks in the process. Pledges of policy stimulus from the heads of the European Central Bank and the Bank of Japan pressured both the euro and the yen, leaving the U.S. Moves elsewhere were muted and MSCI’s broadest index of Asia-Pacific shares outside Japan eased 0.27 percent.