Classical integration sums smooth and predictable quantities, like accumulating steady bond interest, and is visually represented by the area under a smooth curve. Stochastic integration sums highly irregular, random movements, such as wild stock price jumps, and is visually depicted as summing areas under a jagged, erratic path.
Conditions: Classical integration applies to deterministic, smooth functions.; Stochastic integration applies to processes with non-smooth, random paths.
Classical integration sums smooth and predictable quantities, like accumulating steady bond interest, and is visually represented by the area under a smooth curve. Stochastic integration sums highly irregular, random movements, such as wild stock price jumps, and is visually depicted as summing areas under a jagged, erratic path.
Conditions: Classical integration applies to deterministic, smooth functions.; Stochastic integration applies to processes with non-smooth, random paths.