{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T11:03:42Z","timestamp":1751281422193,"version":"3.38.0"},"reference-count":23,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RDA"],"published-print":{"date-parts":[[2023,10,20]]},"abstract":"<jats:p>The paper gives discrete conditional integration by parts formula using a Malliavin calculus approach in discrete-time setting. Then the discrete Bismut formula is introduced for asymmetric random walk model and asymmetric exponential process. 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